With drip you might want to water 2-3 times a week. Apply about one gallon per square foot per week total. So if your tree canopy is about 10ft by 10ft apply 100 gallons per week if there is no rain. That's about 1.6 inches per week. Subtract off any rainfall. If your peaches end up big and not sweet enough cut back to about 2/3 and see how that goes.

Thank you very much fruitnut for the helpful advise, I have been overwatering which is I have read can result in lots of problems.

I didn't want to answer your question because I know nothing about how drip systems affect the volume required, but I do know that a lot depends on weather conditions- humidity and wind, the length of days at the time, and soil conditions(the soil resevoir is usually based on texture but steepness, hardpans and outcrops can matter even more).

If the soil allows a lot of water to absorb rapidly, you'll get a lot more bang for the buck from heavy rains and need less water in between. If an area is sheltered from winds a lot less evaporation occurs. Some soils block easy absorption of water as well, for complicated reasons not pertaining to texture.

Point is, there is no recipe that works for all conditions and you are well served to get your hands in the soil to determine moisture level- or use a moisture meter- at least until you get a handle on your specific conditions.