I like to tie up an ant with a peacock herl body and a nice full black hackle in the middle and fish it at a slow steady crawl. It hackle makes the body look thick and I think they mistake it for a water beetle. super easy to tie and effective!
I love fishing for bluegills on a foam beetle on a #10-12 hook or a small hopper pattern. Sometimes (if leagal) I'll add a dropper of a hares nymph. I have cought two bluegills at the sametime this way.
Other than the patterns previously mentioned...these flies all can do the trick. I listed links to a few that have worked for me, as well as a general warm water fly tying site with some great bluegill/bass/panfish patterns. I have caught gills and many kinds of panfish on the wiggle tail nymph, spider patterns, and even small kelly green green saltwater poppers that had a hinge between the popper body and the hook with a little green marabou for a tail.
I think bluegill can be automatic some times of the year regardless of what you throw as long as they can get their mouth around it, but other times they can be finicky. So you probably wouldnt go wrong with a bunch of different setups...including a strike indicator with beadhead nymphs/small leeches/snails/damsels/etc.