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Here is a link that might be useful: My Garden Blog

That is not a lot of space to grow all that.

The corn is going to require at least 4'x4', although for best results, you will want to use the whole 4'x8' for corn.

You could conceivably plant watermelon on the perimeter, and wrap them around the base of the corn plants, but that won't really leave any space for the onions.

The other option is to orient the bed East-West. Plant the corn on the EAST side of the bed in a 4' x 4' block (this could be expanded to 4'x5' or 4'x6' for better results.) Plant the watermelon on the WEST half along the NORTH side on a trellis. Train the watermelon to grow vertically up the trellis. Give them at least a foot of ground space per plant. In the remaining space, plant the onions.

Most people will tell you though, that there really isn't enough space for all of that in a 4' x 8'. Corn is a GIANT space hog. I gave up on it a few years back, because the space it takes up just isn't worth the yield that I get. I'd much rather buy my corn at the local farmer's market and grow more tomatoes, squash, and other high yield plants in its place. (But I have a very small garden in a very small suburban backyard.

I too gave up on corn, but you could plant the back 4x4 with corn, the vining plants around the edge of the front 4x4 with the rest in the middle. It could work, but I'd worry that the vining crops would block the sun for the onions. GL and take pics so we can see how it turs out!

Here is a link that might be useful: Sinfonian's garden adventure!