Bryan Garner, Garner's Modern American Usage, second edition (2003) offers the following discussion of how to handle possessive proper names ending in -s:
POSSESSIVES. A. Singular Possessives. To form a singular possessive, add 's to most singular nouns—even those ending in -s, -ss, and -x (hence, Jones's, Nichols's, witness's, Vitex's). ...
There are four exceptions to this rule: (1) The possessives of personal pronouns do not take apostrophes (ours, yours, its, theirs). ... (2) Biblical and Classical names that end with a /zəs/ or /eez/ sound take only the apostrophe: Aristophanes' plays[;] Jesus' suffering[;] Moses' discovery[;] Xerxes' writings[.] No extra syllable is added in sounding the possessive form. (3) If a corporate or similar name is formed from a plural word, it takes only the apostrophe. Thus General Motors makes General Motors', not General Motors's ... (4) According to traditional rules, a sibilant possessive before sake takes merely an apostrophe, without an additional -s—hence for appearance' sake, for goodness' sake, and for conscience' sake.
The Chicago Manual of Style, sixteenth edition (2010) reverses the guideline that its predecessors promoted in precisely the area that the poster asks about. Here are the relevant subsections of Chicago 16:
7.16 Possessives of proper nouns, letters, and numbers. The general rule [to add -'s to create possessive forms] extends to proper nouns, including names ending in s, x, or z, in both their singular and plural forms, as well as letters and numbers. SINGULAR FORMS [examples:] Kansas's legislature[;] Tacitus's histories[;] Chicago's lakefront[;] Borges's library[;] Marx's theories[;] Dickens's novels[;] Jesus's adherents[;] Malraux's masterpiece[;] Berlioz's works[;] Josquin des Prez's motets[.]
...
7.18 Possessive of names like "Euripides." In a departure from earlier practice Chicago no longer recommends the traditional exception for proper classical names of two or more syllables that end in an eez sound. Such names form the possessive in the usual way (though when these forms are spoken, the additional s is generally not pronounced). [Examples:] Euripides's tragedies[;] the Ganges's source[;] Xerxes's armies[.]
Exceptions to the General Rule
7.19 Possessive of nouns plural in form, singular in meaning. When the singular form of a noun ending in s is the same as the plural (i.e., the plural is uninflected), the possessives of both are formed by the addition of an apostrophe only. ... [Examples:] politics' true meaning[;] economics' forerunners[;] this species first record (or, better, the first record of this species)[.]
The same rule applies when the name of a place or an organization or a publication (or the last element in the name) is a plural form ending in s, such as United States, even though the entity is singular. [Examples:] the United States' role in international law[;] Highland Hills' late mayor[;] Callaway Gardens' former curator[;] the National Academy od Sciences' new policy[.]
7.20 "For ... sake" expressions. For the sake of euphony, a few for ... sake expressions used with a singular noun that ends in s end in an apostrophe alone, omitting the additional s. [Examples:] for goodness' sake[;] for righteousness' sake[.] Aside from these traditional formulations, however, the possessive in for ... sake expressions may be formed in the normal way. [Examples:] for experience's sake[;] for appearance's sake (or for appearances' sake {plural possessive} or for the sake of appearance)[;] for Jesus's sake[.]
Having laid out those particulars, Chicago 16 also acknowledges an alternative rule that would reverse its main guideline on proper names:
7.21 An alternative practice for words ending in "s." Some writers and publishers prefer the system, formerly more common, of simply omitting the possessive s on all words ending in s—hence "Dylan Thomas' poetry," "Etta James' singing," and "that business' main concern." Though easy to apply and economical, such usage disregards pronunciation and is therefore not recommended by Chicago.
Of course, Chicago's new guideline 7.18 likewise disregards pronunciation—and yet it is not therefore not recommended by Chicago.
Words into Type, third edition (1974) offers these guidelines on "formation of the possessive case":
Proper names. The possessive form of almost all proper names is formed by adding apostrophe and s to a singular or apostrophe alone to a plural. [Relevant examples:} Jack's[;] James's[;] the Davises'[;] Burns's[;] Marx's[;] Schultz's[;] Dickens's[;] Adams's[;] Schultzes'[.] Wherever the apostrophe and s would make the word difficult to pronounce, as when a sibilant occurs before the last syllable, the apostrophe may be used alone. [Examples:] Moses' laws[;] Isis' temple[;] Xerxes' army[;] Jesus' followers[.] ... By convention, ancient classical names ending in s add only the apostrophe to form the possessive. [Examples:] Mars' wrath[;] Achilles' heel[;] Hercules' labors[.]
The problem with this treatment is that all of the "difficult pronunciation" examples involve vowel-s-vowel-s names (Moses, Isis, Jesus) and all of the "ancient classical names" examples involve mythological figures (Mars, Achilles, Hercules), so we don't have explicit guidance on whether Euripides (for example) would qualify as "difficult to pronounce" in possessive form (probably not) or as an "ancient classical name" (maybe).
The Associated Press Style Book and Briefing on Media Law (2002) endorses a rule that looks a lot like the "alternative practice" mentioned disapprovingly in Chicago's section 7.21:
SINGULAR PROPER NAMES ENDING IN S: Use only an apostrophe: Achilles' heel, Agnes' book, Ceres' rites, Descartes' theories, Dickens' novels, Euripides' dramas, Hercules' labors, Jesus' life, Jules' seat, Kansas' schools, Moses' law, Socrates' life, Tennessee Williams' plays, Xerxes' armies.
And finally, The Oxford Guide to Style (2002) has these relevant guidelines for forming possessives of proper names ending in -s:
Use 's after non-classical or non-classicizing personal names ending in an s or z sound: Charles's[;] Marx's[;] Dicken's[;] Leibnitz's[;] Onassis's[;] Zachariasis[;] Collins's[;] Tobias's[.] While convention allows latitude in possessives (e.g. the additional s is used more in speech than in writing), the possessive misconstruction Charles Dicken's is always incorrect.
An apostrophe alone is also permissible in after longer non-classical or non-classicizing names that are not accented on the last or penultimate syllable: Nicholas'(s)[;] Barnabas'(s)[;] Augustus'(s)[.] Jesus's is acceptable in non-liturgical use. Jesus' is an accepted archaism—Good friend for Jesus' sake forbear—and Jesu's is also possible in older contexts.
Use an apostrophe alone after classical or classicizing names ending in s or es: Arsaces'[;] Ceres'[;] Demosthenes'[;] Euripides'[;] Herodotus'[;] Mars'[;] Miltiades'[;] Themistocles'[;] Venus'[;] Xerxes'[;] Erasmus'[;] Philip Augustus'[.] This traditional practice in classical works is still employed by many scholars. Certainly follow it for longer names (though Zeus's, for instance is possible), as well as for post-classical Latinate names favoured throughout the Middle Ages. ...
Use 's after French names ending in silent s or x, when used possessively in English: Dumas's[;] Descartes's[;] Hanotaux's[;] Crémieux's[;] Lorilleux's[.] However, since appending the plural s would be grotesque (Lorilleuxs) or misleading (Dumass), the singular possessive is treated like the plural, for example both Lorilleux's (not Lorilleuxs') cat, the two Dumas's (not Dumass') novels.
Conclusions
Style guides are all over the place on how to handle the possessives of singular proper names—especially singular proper names from antiquity. In the specific instance of the possessive of Aeneas, this is approximately where the style guides I consulted come down:
Garner's Modern American Usage: Aeneas's [because, although it is a classical name, it ends with neither a /zəs/ nor a /eez/ sound; instead it ends with /əs/]
Chicago Manual of Style, fifteenth edition and earlier: Aeneas' [because that is the traditional handling of the possessive for classical names]
Chicago Manual of Style, sixteenth edition: Aeneas's [because Chicago 16 breaks with the guideline in previous editions on this point]
Words into Type: Aeneas' [because Aeneas is an ancient classical name ending in -s]
Associated Press Style Book and Briefing on Media Law: Aeneas' [because that's AP's standard approach to any singular proper name ending in -s]
The Oxford Guide to Style: Aeneas' [because Aeneas is a classical or classicizing name ending in -s or -es]
This list shows considerable support for Aeneas', but it is worth noticing that both Garner and the current Chicago—which carry considerable authority in publishing houses in the United States—favor Aeneas's. If you are supposed to follow one of these style guides, your course is clear; if not, you have some research to do (if some other authority controls your style choices) or a decision to make (if you're on your own).