Hi, thanks for the question.

Watermelons have a range of "days to maturity" from 65 to 90+ days.  This is a rather vague term but can give you a relative idea of how long it takes to grow a plant to get mature fruit.  Starting plants indoors can help by about two weeks over direct seeded. Watermelons that have shorter "days to maturity" are your best option.  Most are on the smaller size. Here are a few varieties to consider. 

• Natsua Cocoa   65 Days
• Mini Love   70 Days
• Sugar Baby   75 day

Soil temperature and other factors can play and important part in early development and at transplanting time. Take a look at the following links for more information:

Watermelon in the Garden (usu.edu)

Growing melons in the home garden | UMN Extension

I hope this helps.