Your description reminds me of Black Rot (Didymella bryoniae). It can enter the plant through damage (bug bite, scratch, etc) in the rind of the fruit, usually forming a tiny black dot on the outside. When the fruit starts to shrivel up and the fungus has multiplied enough on the inside, the black dot on the outside of the fruit where the fungus entered will enlarge into a large brown or black spot.

Black Rot doesn't have to enter through the fruit. In my experience, though, it just usually does. It can enter anywhere on the plant. If it enters through the leaf, it will have a very noticeable black spot. On the stem, a small dark canker.

If this is Black Rot, a general purpose fungicidal spray (add a sticker spreader) should help prevent new disease growth from taking place. Burn, do not compost, any diseased plant material, as the fungus can overwinter quite easily.

This may not be Black Rot. It may be something else. If you don't mind using chemicals on your plants, I recommend for all cucurbits with unresolved disease problems, to add copper sulphate, boron (borax), and calcium to the soil prior to planting; spraying the plants with a general purpose fruit spray (same spray as for apples, etc) when the bees aren't out (early morning or after sundown); and dust with bordeaux. That should take care of most bacterial, fungal, and insect problems.

Good luck.