Think you'd be best served checking local farmers' markets or your state university's/county agent's cooperative extension. The switch over to smaller (less tasty IMO) seedless watermelons started some years back and there are few American farmers that haven't joined in. The varieties you are looking for are..Jubilee, Georgia Rattlesnake and something that has either Charlotte or Charleston in it's name. The 701 or 710 (getting older is not for the weak) isn't quite as good (again IMO) but is still better in taste than the smaller rounder melons. Or just ask them about picnic melons.
No idea about corn uhm well as I really don't eat it UNLESS I can put a pot of water on to boil, run to the field and pop it in the pot in 5 minutes flat.
HTH and GL!