I'm not too sure about small melons other than cantaloupe. You could try sugar baby watermelon I suppose, they stay pretty individual sized.

Me personally, I have crimson sweet watermelon growing on a trellis. They can get 20 to 30 lbs but I set up a support system to hold the melons. First year trying it, and I just now an getting golf ball to tennis ball sized melons, but in theory I think it will work out great.

Simple A frame with cattle panels. Crimson sweet watermelon growing up the left side, and cantaloupe growing up the right side. I cut off the bottom two rows of sideways wires in between each of the vertical wires with bolt cutters and used the remaining vertical wires as stakes to anchor the panels. Once a melon begins to grow, it falls into the middle and I cut two pieces of 1/2" emt conduit long enough to span across and rest on the panels. I zip tied them in place on each side so they don't move. Rest the melon on top and it has plenty of room to grow with no stress on the vine. Also, as an added benefit, they stay in the shade so you have no worries of sun scald. Hope this helps you and broadens the horizons of anyone worried about what they supposedly CAN'T grow vertically :-)