I assume you're considering the Calaveras County Frog Jumping Jubilee, based on the nature of your questions. The lab and I were out there back in 2009, presented our early analysis a few years ago at a few conferences, and we're working on getting the paper out soon.

Unfortunately, there's no species that'll give you a huge edge. The winning Calaveras jump is around 21 feet straight-line, meaning a minimum of 7 foot jumps are needed, which is pushing it even for Litoria nasuta. In general, frog jump distance increases slightly less than isometrically but with a slope higher than zero, meaning that bigger frogs jump longer absolute distances but shorter relative distances, all other things being equal. Many years ago, someone brought Goliath frogs, but only one was small enough to fit on the jump pad, and its endurance was so terrible that it refused to jump at all in the finals. All the other frogs around bullfrog size are either terrible jumpers (pyxies, cane toads) or so similar in morphology that I doubt they'd give you an edge. Many treefrogs are excellent jumpers, but all but the very largest run afoul of the 4" rule.

Given that the teams who compete each year bring hundreds of frogs (allowing them to win based on that 1 in 1000 truly amazing individual) and have spent decades refining their techniques, winning is a long shot. But I definitely highly recommend going and jumping some of the "rental frogs" just for fun - it was tremendously fun to be there, even if I did have to spend way too much time taking notes and hauling around giant PVC calibration grids.