Low Coolant Light Keeps Going On and Off

I need help. I had my coolant replaced because the color was black. After it was replaced, the low coolant light keeps coming on and off. I checked the level and have to replace the coolant in both the radiator and reserve. I have not been able to find a leak. I went back and replaced the new coolant with the Dex Cool to see if that would help. So far, no luck. Yesterday, I found a leak underneath from the catalyc(?) convertor of water. Also, I have started to notice white smoke coming out of the tailpipe. Any suggestions on what I should do? For now, I just keep adding coolant (the one that mixes with all colors).

I'm not clear: Does the light go on only when the coolant is low? If so, it's doing its job.

Pressure test the cooling system. You'll find the leak. White smoke would indicate a leak into one or more of the cylinders.

I have to add a small amount of coolant each time the light comes on to the radiator and completely fill the reserve. I have heard you can put some stop leak in the system, is this a good idea?

no, that liquid copper stuff is totally not a good idea at all. Read the forums, someone on here actually used it to stop an oil leak I think, and it ended up blocking an oil passage way, so the oil pressure went up. I think thats what happened, And somehow he eneded up breaking his crankshaft. Read the post, its quite interesting, I think its called broken crankshaft or something. Just try a search for that. Sounds to me like your herad gasket or a lower intake gasket might be leaking coolant into one of the cylinders and burning it off. You said it was black before changed? Was it filled with oil? Is that what caused the blackness? Have you checked your oil lately? Is it oil, or chocolate milky substance?

I think the coolant was black because it was very old. I just got the car about 2 months ago. I checked the oil and it is fine. I will have somoene check the things you suggested. Before, I messed with it, it was fine. Most recently my anti brake light will not go off. So more problems are starting to occur. Thanks for the info.