I call Lepomis cyanellus the "meanie greenies" for a reason. They are fascinating to watch, but they are the most aggressive Lepomis species. Actually, their aggression is part of what makes them so interesting. In a big enough space or with enough of them to dilute the aggression, you can keep greenies in a shoal. However, if they feel somewhat crowded, or if their aggression can't be spread out among many individuals, then one can overwhelm the others and become hyperdominant. The trouble with keeping them in a group, is that unlike other sunfish, greenies aren't really a shoaling species. And with that big, bass-like mouth, they tend to act a bit more like basses, preferring to hang out by themselves in a small, sheltered area to stalk prey, rather than swim about in the open feeding on plankton like bluegill. I've tried keeping greenies in small groups (2 or 3), but this always failed due to bullying, so if you were going to try and shoal them, it would have to be in groups of 6 or more. But then you won't really get to see their cool, natural behaviors, so IMHO it's better not to try and shoal them. I've also tried keeping them with bluegill, but the greenies overwhelmed their cousins (which aren't wimps), so I ended up separating them.
I also went through a phase years ago when I tried keeping greenies with cichlids (which I no longer do). I had one setup with a small Texas cichlid and two small green sunfish. The two species do coexist in Texas, but they didn't set up a stable hierarchy for me and kept fighting, so I separated them. In another setup, I had a 5-inch green sunfish who peaceably dominated a convict that was a bit smaller, and got along okay with a similarly sized Jack Dempsey. However, he amazingly dominated an 11-inch oscar, which was up to that point the benevolent dictator of the tank. At the same time, he kept scrapping with a jewelfish, and getting his pectoral fins tattered, which was not good. So, I put him in an adjacent tank to live by himself, only interacting with the cichlids safely through the glass.
In the past, what has worked was keeping one green sunfish with one black bullhead catfish of similar size (these two species also coexist in nature). The two got along fine and mostly stayed out of each other's way, just as cichlids and catfishes usually do. The only problem would be if the bullhead eventually gets big enough to eat the green sunfish, but as long as they are of comparable size, I think the two get along fine. Currently I have one greenie in a 55-gallon tank all to himself. I've thought about putting a bullhead in there with him, but am reluctant to do so because bullheads need a bigger tank than that. So for now, I guess he'll have to continue to be a singleton.