This could be any number of things. Take a look at the information below and see if anything resembles what is happening on your peach trees.
Trees will exhibit an oozing, clear gum-like sap when peach tree borers are present. Try scraping off the good and see if you find entrance holes and borers inside the tree. The following article discusses peach tree borers and will give you other signs to look for:
Aphids could also be the culprit - they secrete a sticky fluid called honeydew.
It could also be bacterial canker. For more information on bacterial canker, visit the link below: