Well, goldfish is a tricky fish. Unless you stock lots of predators, you won't reduce their count. Actually yellow perch won't do much harm to them simply because of it's mouth size. It's not large compared to an average goldfish. Sure, they will eliminate juveniles but large spawners will survive and continue spawining each year.
I don't quite understand why are frogs so important but that's not my business. I don't want to disappoint you but I have to admit that frogs usually are quite a nice meal for predators. Perch, pike, catfish etc. eat them... Sure, perch will eat smaller ones while pike is capable of eating large specimens as well. I've heard that catfish (in my case WELS but maybe the same can be said about other catfish as well) prefers frogs rather than fish that are eaten only because frogs are not always available.
But you won't get rid of frogs anyway. Probably you know some pond or lake with lots of predators, don't you? Haven't you see frogs there?
