since don't know the variety that really is a problem because several varieties of watermelon normally have yellow spots on the leaves. But since have not given enough information about the plant or the spots I really can not give you an answer. well best luck next time provide more info.

We've had a very dry and hot spell but, but it started cooling off pretty fast. From nightly temps in high 80s all summer to now sudden temps in 40s and 50s at night. After the temperature change is when this started showing up. They were watered and looked healthy, aside from some aphid damage, through all the hot weather. The cooler weather also seems to have gotten rid of the aphids.

I agree with Keriann. Yes, you should really let them dry out. Matter of fact, once my seedlings are as big as yours, I let them dry out pretty much all the way before I water again. You can tell they need watered when you pick up the flat and it feels light as a feather. Then after you water, it's much heavier. Your method of bottom watering is quite unique, I must say. I think that most folks bottom water the way I do, which is to say setting the cells or cups into a tray of water and letting the plant absorb as much as it wants until you see moisture on the surface of the soil (usually takes anywhere from 5-20 min). Now, I can't say for sure what positive or negative effects your method of watering might have, except that it sure sounds like a pain in the hiney to me, and I somehow doubt that the soil is getting properly saturated. You want to simulate mother nature; a soaking rain. Then you want to let the soil dry out. That's how it is in nature. Roots need water yes, because the plant needs water, but then they need to dry out and get oxygen. Damp soil all the time = no oxygen to the roots. Now, I can't say for certain what part of your program is causing your issues, but I would start bottom watering them as described by letting them absorb water sitting in a tray. I think you will find that using this method, you should only have to water every 3-4 days, or less. I would lay off the ferts for a while, and then make sure only to fertilize when the soil is already damp, or you will burn the roots. I just mix the fert with water, then pour into a tray and bottom water as usual. Give this a shot, see if that doesn't help.

What did you use for the Aphids? Leaves turn yellow, exhibit chlorosis, for many reasons and sometimes people spray inappropriate things on plants to eliminate Aphids that cause the plants leaves to die, which yours are doing. If something was sprayed on those leaves that restricted that leafs ability to breath or photosynthesize the plant will cut off nutrient flow to that leaf and it will die.