I think it is most likely a partial rhyme; the vowel sounds may have been somewhat closer than they are today, but not identical, and probably not even nearly identical. Watts seems to have been working in a poetic tradition where vowel sounds did not have to match perfectly to be used as rhymes. (Systems of 'imperfect' rhyme are well exemplified in modern English song lyrics of various genres, although of course the details differ). It is possible that in some cases not only the sound, but either the etymological kinship of certain vowel sounds or their similar spelling ("eye rhyme") made them more amenable than any random pair of vowels to be used as rhymes.
I wrote an answer to a related question about Pope: Pronunciation of "lost"
In Middle English, before the "Great Vowel Shift", the difference between the vowel of wax and the vowel of make was solely one of length.
The Great Vowel shift caused both vowels to assume a more "close" or "raised" pronunciation (with a more raised tongue, which makes the mouth less open); the long vowel in make ended up becoming a more close/raised vowel than the short one in wax.
Per the timeline at Wikipedia, around 1715 the vowel in makes might have been something like [ɛː] or [eː]*, vs. [æ] in wax.
While not incredibly close, these are somewhat similar: both are unrounded front vowels, and unlike the usual modern [ei̯], neither is a diphthong. Perhaps more importantly, the spelling and the example of the usage of prior poets for which the pair may have been simply [æː] and [æː] (such as, perhaps, Shakespeare) may have caused Watts to consider these vowel sounds close enough to make for an allowable rhyme.
The Oxford English dictionary does record pronunciations of make with a shortened vowel /æ/, saying
The α forms with a short a must have arisen in Middle English before the great vowel shift. J. Wright, Eng. Dial. Gram. (1905) records such forms from the northern counties and as far south as Shropshire, Staffordshire, Warwickshire, Leicestershire, and Lincolnshire; in Scots, the pronunciation /mak/ is general.
Isaac Watts was born in Southampton, Hampshire; I am not sure if this is too far south for /maks/ to be a plausible pronunciation in his mouth.
The OED also records forms of make with short /e/~/ɛ/, but I don't think that is particularly more likely than a long [ɛː] or [eː] to have been the pronunciation Watts had in mind.
I assume that "bee" in the first line and "day" in the third constituted a partial rhyme for Watts (the original vowel of bee is different from that of tea). If I'm correct, this would provide evidence that he made use of the license of rhyming on non-identical vowels.
His hymns also provide pairs such as the following, unlikely to all be full rhymes:
*That is, with a lengthened version of roughly the sound of the vowel used in the word DRESS. Although the English TRAP and DRESS vowels don't necessarily sound particularly similar to native English speakers today, Germans and Russians among others notoriously have tended to have difficulty hearing a difference between the English TRAP and DRESS vowels. Furthermore, many modern accents use a lower or less fronted value for TRAP vowel than was previously common; although often still transcribed "/æ/", the TRAP vowel in modern standard Southern British English is, per Geoff Lindsay, more accurately transcribed as [a].