Ben,
I don't want to rain on a parade but you should take a realistic look and maybe make some true take-offs of power from your 'merry-go-round' before you build something not so merry that won't be used to go round.
World class athletes have trouble maintaining 300 Watts of power. I don't think a batch of kids will be able to give that output and you harvest energy both. A simple, adjustable brake might give you an idea how much power is available for harvest. This same number will also dictate a lot of the design of the proposed alternator.
I suspect one of the most practical drive systems will be a 'serpentine' style belt as used on modern automobiles to drive accessories. One could roll the drive pulley of steel or turn it with hand tools of made of wood. The driven and slack take-up pulley would be sourced from a salvage yard. This 'start' would give one the opportunity to gather output information.
My first inclination for the power end would be a permanent magnet conversion of a small 3 Phase motor. There would be several voltage connections available. The belt-pulley ratio could be easily changed for desired voltage. Possibly, a controller could harvest variable amounts of power when it was possible.
Good luck,
Ron