sbyerb,

"disease resistant peach" covers a lot of ground, because there are lots of diseases. I'll take a shot in the dark since you're not getting any fruit, the disease you want rid of is brown rot. It's generally the one that can completely destroy fruit.

There are some varieties more resistant to brown rot than others (see link below) but even with them, I'd be surprised if you could get by without spraying. Given your location, insects are probably an issue as well.

What and when are you spraying?

Here is a link that might be useful: Table of resistant peach cultivars

Olpea is a highly competent poster, but may not be sensitive to the intense disease pressure we face in the hot, humid south. Brown rot can be effectively controlled with good sanitation practices and a pre-harvest spray of Captan or Immunox. Our bigger problem here is bacterial spot, whose primary control is through disease-resistant cultivars, such as Redhaven(yellow)or Belle of Georgia(white). There are other fine choices, too.

But, like Olpea, I can only speculate without additional details from you. Can you give us a little more to go on?
Misterbaby.