I'm just shooting from the hip here, I've never installed an air conditioner or built a ground source heat pump. The ground temperature in my region was around 60F and it's probably higher in Alabama, so it would you would have to circulate a LOT of water and your blower would have to run constantly to do much cooling. The reason is, although a water radiator would absorb a lot of heat, an air conditioner coil absorbs much more because the liquid in it boils at a cold temperature that can then discharge the heat into the ground loop.
I would think to cool with water would require very cold temperatures, much colder than ground temperature. You might want to think about installing a ground source heat pump depending on the installation costs and soil type in your area.
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