Having never had this problem with my grapes, I would suggest that you cut off a sample and take them to your closest University Ag Extension office. They would know what is going around and could suggest a cure. Offhand, I think you have a fungus.
you have black rot..... not much you can do now, but carefully prune out the whole bunches
pick up all the grapes that have fallen on the ground and spray with copper<Bordeaux> as a fungicide.
google black rot on grapes there are quite a few articles on this..
yep, you have black rot. you still want to report this to your local coop extension so they can keep track of reports for the area. black rot is a fungus and you will need to start using a copper fungicide spray on them to help get this in check. clean up any dropped fruit and clean any affected bunches. you may still get some bunches that are unaffected but it would be best to just cut all the bunches away and let the vine rest for the year. Bonide makes a spray but i noticed it is not organic, i think it was called Fungoil. you can buy their copper fungicide that can be used as either a dust or mixed into a spray and this is considered an organic product if you prefer this instead.
there are a few grape varieties that are resistant to black rot, it just might take some researching to find one similar to yours. places that specialize in grapes will usually tell you if they have resistance to certain diseases or fungus issues they are prone to. i like DoubleAvineyards.com for their information on the grapes they carry. another good site to check out for grape varieties you can buy cuttings from is Lon Rombough's bunchgrapes.com