-kins (I've only heard it with an s) is arguably still productive, but in very limited contexts - unlike other diminutives, it seems to only be used when an actual small baby is involved, not for mere endearment, though in this context it can be used either for the baby or for the people around the baby.

-let is still productive (applet = small app; even Aplet = candied apple is only documented a century back); only takes ordinary nouns.

-ling feels still productive, but new archetypes are rare so it's mostly used with preexisting words.

-ole and variants might be productive in science but are otherwise not even recognized.

-poo is apparently productive but not something I ever reach for

-ses I'm not convinced is actually correctly analyzed; it appears to just be a redundant plural, similar to how "bestest" is a redundant superlative

-sies is actually just -s (diminutive/filler) + -ie/-y (diminutive) + -s (plural). Usually the first -s is required for a word that ends with a vowel (but also after n (including nd/nt with the d/t weakened), m, ng, r, l, p, or b; the need for disambiguation is also relevant)

But -y/-ie remains by far the dominant diminutive. It shouldn't be confused with several other uses of the suffix though (such as with the meaning of -ish).

Influence from Romance languages is strong enough that foreign diminutives are now more common than some of the traditional English diminutives.