water melons

Midge, watermelons need a long hot season to grow and ripen fruit, usually 80-120 days. Unless you are in an area that gets a lot of sun, I don't think without a greenhouse you will have much success.
If you care to try, start seeds indoors next spring of a variety that takes a short season. If you can, use artificial heat to get them sprouted, when temps are warm outside, put out in the sunniest position you can find.
It won't be easy, but you could try it. A good person to ask for advice is David, he has grown a lot of heat loving plants in Scotland, he may have some better tips for you.