The suffix -een does exist as a suffix in English, but it is not a very common one, and it is not really productive outside Ireland. Even in Ireland, it enjoys only limited productivity.
The suffix comes from the Irish Gaelic diminutive suffix -ín, which does indeed indicate that something is small and endearing. Like Romance languages, Irish has quite a few different diminutive suffixes that can be employed fairly freely. -ín is probably the most frequent one, but other very common ones are -án (which was originally only a diminutive, but is now more common in forming other types of words) and -óg (as in seamróg, which is Anglicised as ‘shamrock’—it’s nothing to with rocks, just a diminutive of seamair ‘clover’, with the Irish -óg replaced by the formerly common English diminutive -ock).
In Irish, it can be added to both common nouns and proper names (both male and female, similar to -y/-ie in English), but since it is so productive and common nouns outnumber proper names by a factor of something very high, the number of common nouns in -ín is of course much higher than the number of proper names in -ín. Wiktionary has a whole list of Irish words with this suffix, and many more can be made on the spot.
It is also frequently used to represent the very common English diminutive(-ish) suffix -ing, such as in góislín ‘gosling’ or féirín ‘fairing [gift bought at a fair]’.
The diminutive -een suffix borrowed from Irish doesn’t appear in many common nouns in English, at least not words that are used much outside Ireland. Even in Ireland, the number of common nouns suffixed with -een is fairly small. Girleen is one of the ones you’ll occasionally hear in Ireland, but I’ve never heard it anywhere else. A more common one found both in and outside Ireland is colleen, which is a direct Anglicising of Irish cailín ‘girl’, a diminutive of caile ‘girl, wench’. (Bizarrely, colleen is missing from the list of English words suffixed with -een on the Wiktionary page.)
Quite a lot of the proper names that are suffixed with -ín in Irish, however, have corresponding English forms in -een (and one or two common Irish nouns have been reinterpreted as proper names in English), but they are all female names. Male names are never diminutised with -een in English, unlike in Irish. The reason for this is probably that there is a French suffix -ine, which is exclusively feminine and frequently appears in personal names as well; it means something like ‘belonging to’ or ‘showing traits of’, which is a common way of forming personal names.1
In Irish, when they borrowed French names with this suffix, it just merged with their own diminutive suffix and it wasn’t so very strange that all the French ones happened to be feminine—the Irish one was still perfectly useful for both genders still. In English, however, there was no indigenous suffix for -ine to merge with, so it remained limited to its feminine usage in French. By the time the Irish names suffixed with -ín started being borrowed into English, the /iːn/ suffix was apparently already so fixed from French as a feminine suffix that the male names thus suffixed were just not borrowed.
So English has personal names that end in /iːn/ from (at least) two different sources, Irish and French, and many of them are tangled up enough that it’s hard to know which of the two is the more relevant origin of a name. Some examples:
- Colleen, from Irish cailín ‘girl’ (see above)
- Maureen, from Irish Máirín (diminutive of Máire ‘Mary’)
- Eileen, from Irish Eibhlín (from French Aveline)
- Laureen, from Irish Láirín (diminutive of Lára ‘Laura’) and/or French Laurine
- Cathleen, from Irish Caitlín (from French Cateline, a variant of Catherine) and/or French Cateline
As mentioned above, though, the suffix is not really productive in English. If you’re in Ireland, you may get away with forming such nonce uses as lasseen (‘wee lass’ = little girl) in conversation, but generally you’re limited to using the words that already exist, like girleen (little girl), maneen (little man), poteen (moonshine), velveteen (a type of fabric), spalpeen (rascal), etc. None of these are particularly common words, either.
If you used it productively and talked about your dear little careen (car), most people would probably be quite nonplussed and not know what you meant.
So yes, it is a diminutive suffix that signifies endearment and smallness—but it is not a productive one, and using it as such would not be natural and would most likely just confuse people.
1 The French -ine suffix also shows up in common nouns as well, and it is variously spelt -ine (as in heroine, medicine, etc.) and -een (as in canteen and tureen). The French suffix shows up, as you can see, in many words that are far more common than the ones containing the Irish -ín suffix.
The French suffix is inherited from the Latin suffix -īnus (> French -in), feminine -īna (> French -ine). This is ultimately cognate with the Irish -ín suffix (which is from Proto-Celtic *-īnos), as well as with English -en (as in ‘wooden’), Greek -ῑνος, and a host of other similar suffixes throughout the Indo-European languages. The ultimate origin of the suffix isn’t entirely clear: the commonly reconstructed Proto-Indo-European form is *-iHnos; it may or may not be somehow related to the so-called Hoffmann suffix *-h₃onh₂-.