I think that cherrry trees ooze a clear kind of sap that looks like silicon gel anytime they get cut. Perhaps it is infested with some sort of bark boring beetle or something else. Are there woodpeckers there, or signs of their holes under the ooze? These are just guesses. It seems to me that something must be puncturing the bark.

I do not have direct experience with Cherry trees but what you are describing sounds like
it may be bacterial canker:

oozes a heavy gum in spring and fall
leaves wilt and die in summer
Fruit may get infected and has darkened depressions on the skin

There is only one way to cure bacterial canker:
cut out cankers and paint wounds with a 1:1 mix of lime sulfur and white latex paint
after removing each canker disinfect hands and tools in a bleach solution (1 part bleach to 4 parts water)

If an entire limb or shoots are infected and can not be saved than remove them completely and burn them if possible or dispose of them in a sealed black plastic garbage bag.
If this is your problem and this method does not work than the entire tree will probably need to be destroyed.

Perform Maintenance each year and clean up all debris around the tree. Take your leaves in for analysis of nutrient levels and correct soil deficiencies. Use a Kelp spray to help restore the trees vigor while it comes back into balance.

If the tree needs replacing consider a resistant varity like Stockton Morello