What you have sounds like BER for Watermelon's..
**Blossom End Rot**
BER or Blossom End Rot is caused by a lack of calcium in the developing fruit.
This can be from either it not being in the soil and/or available to the plant
Or when the watering is inconsistant..
Like tooo much water, then a dry spell, irregular watering habit's or practice's or naturally accuring with or without rain...
You can use Dolamite Lime *to sweeten the soil*
***Have you done a soil test to see how your soil is though?????***
Or you can spread/sprinkle some Epsom Salts in the soil and on top of soil, time of planting..
Or even spray of Epsom Salts too on the foliage...