How much water should developing watermelons receive? Other than rainfall?

My watermelon vines are going crazy after the big rain we had last week. I have seen a few baby watermelons just on the one end of the vine, so there are probably many more I don't see. Every day I give each plant a watering can ( 2 gallons) of water, unless it rains. Each time I see the baby watermelons they look a bit bigger. At first, the were the size of a dime. Then a quarter. Then a half dollar, now a silver dollar and bigger. Is that enough water to keep the vine going? How much water should a fruiting watermelon vine recieve to get good melons without them splitting?