How are diminutives formed in recent English words?
Edit: it is important to distinguish between two senses of "diminutive": it can be neutral, as a smaller version of something; or it can be mocking, affectionate, etc; in many cases, a suffix is diminutive in both senses, because the latter often follows the former. I am mostly talking about the neutral sense here, which might not be what the original poster intended.
I'd say there are no truly productive (capable of producing new instances) diminutive suffixes in modern English. As Mitch mentioned, -y/-ey/-ie is the suffix that comes closest, but that is still not quite close when compared with suffixes in other Germanic languages, such as German and Dutch. For one thing, this English suffix is never quite neutral, it is always a bit childish or mocking, etc.. And it can only be used with selective nouns, not just any noun.
Dutch: televisie (regular), televisietje (dimin.) or router, routertje is perfectly acceptable, i.e. it is even used with new words of foreign origin. I believe the same applies to German Fernseher, Fernseherchen, etc..
It should be noted, however, that the diminutive is in many languages inherently a little bit informal, because a smaller version of a normal thing is inherently less "impressive" than the normal thing, unless the smaller version is an old word that has gained some sense of "normalcy", or some distinguishing qualities, through time.
(EDIT: Actually none of groupie, techie, Trekkie, and buckyball are diminutives. Ah well, I'll leave them up in case others are tempted to make the same mistake.)
Here are some words along with year of first known use:
groupie (1966)- techie (1970)
- buckyball (1985)
Also, there is Trekkie, but I couldn't find a "first known use" date. Certainly it can't be earlier than 1967, the year of the show's premier.
Maybe it's because of a mental bias that -ie and -y words are the only ones I've come up with.
FURTHER EDITS
Well, taking a hint from Cerberus: telly (1939) is definitely diminutive, although 1939 isn't exactly the past few decades.
Ah, something five years closer to the present: homey (1944), diminutive form of "homeboy". And a little closer, Yorkie (1946) for Yorkshire Terrier. Closer still, Westie (1959) for West Highland White Terrier.
Found something closer: jammies (1973) for pyjamas. Also veggie (1955) and commie (1940).
Okay, a truly recent diminutive: applet (1990), short for application.