I know what you are talking about. The holes are rectangle about 1x2 inch, you need to measure the width, they taper down toward the bottom but just worry about the top of the hole for now.
If they are 1inch wide, I would go to a big box HI store and buy the oak stair treads. These are true 1inch thick and 4feet long, not sure on the width 12"?
Rip these to the length of the stake pocket hole bottoms, cut these to the desired height plus the depth of the pocket.
The length of the rails is also up to you, you can make the ends flush with the outside stakes or extend beyond might as well stay at 4' width IMO.
Block up cart and level top side edges of trailer, fit stakes into pockets and eyeball them plumb, add exterior carpenters glue to aproxx area of inside of stake about where you want first rail, eyeball rail level and lightly clamp. Tap stakes and rail alternately while holding piece not being tapped so that pieces move independent of on another until stakes are plumb and rail is level. This might be frustrating but if you built it on the ground with measurements between stake pockets and found you were off, it would be more frustrating. Remember glue is drying....when you think it is level and plumb, recheck cart for level and run 2 stainless 2" screws diagonally at each intersection to be able to remove clamps, proceed to the next rail.
If you plan to haul mulch and want to heap it, use plywood or wide plank wood for rails
If the stake pockets are 3/4 inch wide use plain 3/4 oak boards
When its all together and glue is dry, you can back up those screws by 2 more screws or by drilling hole in other corner of intersection and use 2 carriage bolts.
To not go over $20, you either have to find the oak for free or use pine but you will not be happy with the sectional area of pine in that stake pocket for durability.
Paint or stain and poly to you hearts content.
Checking the deere website, gives 3/4 x 2 inch for the stake pocket on the 17P cart 10P is probly the same. Use 1.25 inch screws to fasten two 3/4 boards together.