So sorry. It looks like you have a weeping peach or cherry tree and both of these are susceptible to insects that bore into the bark and the resulting fungal infections. Sometimes sap will ooze if a tree has bark that was damaged by a mower but in your situation I suspect disease. The disease is hard to beat unless you have the tree sprayed with the proper insecticide and in your case I would recommend a professional arborist to decide if the tree is worth saving and if so which pesticide to use. Cleaning up fallen leaves and making sure the tree is not stressed from lack of water or poor drainage are two ways to prevent this infestation in the future. If you do decide to make like George Washington and cut down your cherry (or peach) than remind yourself that you now get to pick out a new tree - but avoid any of the stone fruit trees that are susceptible to the borers. Depending on where you live, a weeping Japanese maple or evergreen dwarf Alberta Spruce are two small trees that could be used in the space instead. Keep growing, Marianne Binetti