At the local building supply, get four 1-inch EMT conduit 90° elbows, enough 1-inch IPS (1.315 OD) chainlink toprail tubing for the sides and ends, and eight 1/4 x1-1/2" round head machine screws with acorn nuts.
Minimum tools are a tubing cutter or hacksaw, a half-round coarse file, a centerpunch, and a drill with 1/4" bit.
The corners go like this:
Below is a simple frame made this way (with the conduit corners pop-riveted rather than pinned with machine screws). The advantage of screws is the frame can be taken apart.
For a stout drop-in rig, you could add four SpeedRail 1" IPS #5 Tee-E fittings (from DRE or Nu-Rail) and crossbars.
To suspend the cooler, use four rigging straps (4-ft. loop straps are nice for the top).
I'd guess you're going to rig it lengthwise, with straps around the thwarts. There were some big paddle-rafts on the Grand set up that way.
Whatever you do, have fun.