Not sure what kind of feeder you bought, but in case it is one of mine here are some things to try and a comment or two.
Bunnies, yeah, more reach than a chicken and heavier than a chicken, no stopping rabbits. I have had people ask me if a rabbit could use our feeder.
Squirrels, if this...
Here is a thought for you on the perching on the tops of the Grandpa feeders, go down to the big box hardware store and purchase a few tin flashing pieces, the L shaped ones. They are cheap, under a buck each. Bend a flange on each end of the L and fasten one or two upside down, kind of like a...