Smaller ones should do well. Many of them do not slip which would be an added advantage on a trellis. Range is about the same as a cantaloupe, 4-7 feet depending on variety.

Thanks farmerdill! By slip do you mean fall off the vine? The variety I have here is Earli-Dew, have you heard of this one?

Yes. Earli-Dew is an early ripening, mid size melon that slips from the vine when ripe. A dependable performer for me.
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I had a volunteer a few years ago, so I don't know the variety, but the vine grew at least 9 feet long. The roots were in a raised bed, but the vines were supported outside the bed on some old border fencing I had so the melons wouldn't be on the ground. They go along the side and around the front of the raised bed in the photo.

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Okay Farmerdill, I looked at your album too. You have quite the variety. You must have a large plot to be able to grow so many varieties. One more question before I leave you alone. How much water do you recon a plant would need per week? I know it would depend upon the weather, etc, but I got a little drip irrigation system and am trying to decide on what type drippers to put on there. I was thinking the 1GPH ones.

Hello 1gteacher, that's what I'm looking for. Some type of growth like that. It's been such a long time since I've grown melons I almost forgot what to expect. Thanks for posting the photo.

I am traditional so in a normal year I rely on rainfall. During this extended drought over the past several years I have had to move the melon patch to an area that I can irrigate. One inch a week is usually sufficient. You want to the soil wet to a depth of 6-8 inches then let the top 3-4 inches dry before reapplying. Drives the root system deeper. Usually when the plants wilt badly in the heat of the day, it is time to apply water, just avoid shallow watering.

Okay, thank you very much. I'll water them very sparingly then. I believe Texas is a little dryer than your neck of the woods, so I can always adjust accordingly.