Don't know how green sunfish are an invasive specie when they are native to the US. Unless they just aren't native to that area. But I could see how they could easily become invasive with how adaptive/predatory they are.
The coppernose are nice looking but we don't get them here. All we got for sunfish species around here are: flier sunfish, green sunfish, pumpkinseed sunfish, orange spotted sunfish, black crappie, white crappie, gluegill, small mouth bass, rock bass, and large mouth bass.
Btw IDK if it's the same over there but in SD here we can't sell wild caught game fish but if it's bred at home then it's legal to sell because it isn't affecting the wild population. It would definitely be worth looking into the legality of the sale of, wild caught vs captive bred, native game fish species. I would imagine it would be the same but I could easily be wrong, it could be either less restrictive or more restrictive.