Since you write that children frequent that area, you might bring the situation to the attention of your city council (contact your councilperson or borough president’s office) for assistance. High concentrations of animal feces can be hazardous to childrens’ health.
They may be able to compel your landlord to keep the area clean. That would put the onus on the landlord to contend with the dog owners and relieve you of having to fight with your neighbors.