They need a LOT of room. 10 gallon pots may seem large but watermelon vines will require watering every day in a ten gallon container because the draw so much water and the large leaves allow a lot of evaporation to come from them. I know there are bush varieties so maybe check out some of those for container planting but those old black diamond variety of watermelons likely won' do well.
This is first time growing them. I did not intend to plant watermelons and don't have experience with them. When I bought the plants I thought they were zucchini and was told so at the greenhouse. I could not find seed of nearly any kind of garden plant in my area. I live in east southern Ohio and didn't get my garden in til last couple days of May which is about 3 wks. late around here. I have a few about 4-5 melons on and the largest is about 8" dia. they appear to be a seedless variety. I planted directly into unfertilized untested ground that had not been planted in before so far as I could tell (I have only live art this place 1 yr). All my plants are doing well but not a lot of fruit as it got very dry here a few weeks after planting. I was told by a former neighbor that this area of Ohio has a great soil ph naturally for gardens he was really in to it.