Deep cycle batteries need a slightly slower charge rate, so the voltage is lower on that setting. 2 amps is a maintenence setting anyway, so you would need the 10 amp position or higher to recharge a dead battery. While it's possible to recharge a dead one with 2 amps, it will take a week or more. As long as the acid doesn't boil out of the cell caps or the battery gets too hot to touch, you're not overcharging. Immediately after starting, an alternator will have a charge rate of 60 amps or more, so a short surge of high current is not harmful. Just don't force a high charge rate into the battery for a long period of time.
If the cells are not sealed, you'll need a hydrometer to check the state of charge. Full-charge specific gravity is between 1.265 and 1.300. A dead battery will have a specific gravity of 1.100 or less, so check the specific gravity every hour until it tops out. At that point, further charging just boils the water away. NEVER add acid to a battery, only clean tap water. Distilled water is best, but anything suitable to drink is probably OK in a battery. Stay away from water with high mineral content, or water that's been stored in a metal container like a galvanized bucket, for instance.
Jerry
