Cherry Tree Growth
From the picture, the ooze is likely caused by the bacteria disease bacterial canker... we see this disease move in during cool wet blooms, but sometimes we see ooze later in the season when it is hot. Unfortunately, there is nothing you can spray for control of this disease--pruning out the branch is the best option. The other possibility is that the ooze is the tree's response to a borer. We have three insect species that bore into cherry--do you see any brown frass or sawdust near the ooze? If so, then the problem is likely an insect. Lastly, in commercial orchards, we see oozing as a response to phytotoxicity--most of the time caused by ethephon. This product helps loosen cherries from their stems, and if sprayed in hot weather, the tree responds with oozing. I doubt that you have sprayed much on your trees, so my guess is one of the first two solutions. Let me know if you want to follow up on this question.