2001 Jeep Wrangler Coolant Leak

I'm leaking engine coolant through my heater core. My radiator has been tested and no leaks have been found. However, I can see coolant dripping from the heater core into my floor boards in the car and onto the ground outside the car. The engine has been overheating and I constantly need to refill the radiator to keep the engine cool.

My question is, how do I stop the leak through the heater core? I know I can bypass it by connecting the hoses but that leaves me without heat in my car. Please help me out if you can. Thanks!