If you can mesure the tank, please post the length, height & width. I agree that silver dollars are schooling fish and BP's certainly aren't, but it depends on the tank size. It'd be really nice if you could take out 2-3 of the parrots and replace them with SDs.
If the tank is bigger than 80g and you can get the number of fish at around 4 SD's and 2-3 BP's, you can try larger schooling fish, like Congo Tetras or Tiger Barbs. Depending on the agressiveness of the BP's, you could or could not add larger (5-7") loaches. The agressiveness of the BP's could be raised by higher than normal number of them.