Big misunderstanding is tank size, IF the compressor can not make more air than the device attached to the end of the hose uses the compressor will run continuously. Only thing a second tank will do is act as an air receiver and let the air slow down in that area, less velocity will give the air a few more moments to let moisture drop out.
Best advice I can give you is to get a spray gun that uses less air than most.
2nd: make a portable cooler for your "system". Buy a coil of 1/2" copper and pull it out like a slinky. Make its overall end to end dimension just less than a 55 gallon drum.
Connect your air compressor to the copper tubing at the top of the plastic drum.
Run the other end of the tubing thru a bulkhead fitting at the bottom of the drum. After the bulkhead fitting install a tee, put the bullhead of the tee on the line coming from the bulkhead and put the tee in a vertical position. run a float type drain off the bottom of the tee, and run your air hose up at least as high as the rim of the barrel. Fill the barrel with water, allow a small flow of water to overflow if your water isn't nice and cold .