Black Diamond watermelon (see above) grows well around here, and the melons are nice and sweet. I have the most luck if I thin the herd (no more than two-three melons per vine, the first one gets most of the flavor and size) and just grow more plants. Black Diamond is normally red fleshed, but is also available yellow fleshed, and I'd like to try that this year. I grew some yellow-fleshed variety five or so years ago, and it was fab.
Source for the red (also Moon & Stars, a bunch of others):
http://www.heirloomacres.net/HeirloomAcres/
Source for both:
http://www.rareseeds.com/catlisting.php?cat=32
Christmas lima beans:
http://www.rareseeds.com/catlisting.php?cat=65
Cob Melon (apparently AKA Schweikert's Cob Melon):
http://www.douglasgould.com/amygoldman/New_From_Amy/melons%20book/cobmelon.htm
this is the variety I've grown before, but not the source of the seed:
Tohono O'odham Yellow Meated watermelon
http://www.nativeseeds.org/v2/prod.php?prodID=G003
one of several sources:
Black Diamond Watermelon
http://www.heirloomacres.net/HeirloomAcres/AddToCart.asp?number=HLAVS219&pkg=Pkt.(50%20seeds)&price=1.25