You can use a simple woven trellis as for peas or beans. The trick is to make cradles to support the fruits; old pieces of the leg part of pantyhose work great.

Thanks but will the vinyl netting hold the heavy fruit?

Yes, vinyl netting is much stronger than it looks. Most are rated to hold up to 70 lbs.

Just a side note, vinyl netting =/= nylon cradles. I've used non-vinyl netting type products in an attempt before, hoping to just compost the whole thing after - it broke down too well to support by the end of the season. The cradling is to hold the melon (or whatever you're growing) up without straining or breaking the vine.
Vinyl netting is great, just make sure it's hung or braced well. :)
I've had good success with chicken wire on pvc, and that I can just put it on rebar supports and move the whole thing elsewhere whenever I need to.

What's your set up like? Are they freestanding boxes? Do you have any sides against a wall or fencing?