M., what is your time frame? I've been doing traditional weekly swim lessons with my 5 and 4 yr old boys. We've been going since September and they're just now competent beginning swimmers. Obviously private lessons you get individual time so the child can progress faster. I believe it the frequency of the lessons, not private vs. class. I've heard Calvin College does summer swim camps of two weeks of daily 1 hour lessons. My sister, who lives in Florida and has a pool in her backyard, did the infant swim program. It's a baby survival swim training. It is expensive! Daily 15 minute lessons until they get it. The child has to be able to fall into the pool fully clothed and get themselves safely to the side before they "graduate." My sister said it was worth every penny.
Good luck.