Hmm well I'm just taking this from memory, but there should be one in Looking In A Thing In A Bag or Cool Things. The only actual instance I can remember of him smiling is during one of the Halloween toons (3 Times Halloween Funjob, now that I've checked), but of course, that's Halloween.
I think what you could probably do is screencap Homestar smiling in the 'ween toon, and then try to screencap him leaning back while he's talking in a normal one (since he does bob around a bit), but that's probably more work than you'd be bothered to put in. And later there should be another person with an actual picture. Good luck though!
Also, welcome new user.
Your carefully worded request that-toes-the-line-between-polite-and-casual is something I do all the time, it's so awesome actually seeing somebody else do it.
