Check the voltage with the engine running - it should be about 13.5 volts. You can run a current test, but if you're getting about 13.5 with the engine running, the alternator is working. Check the cell-to-cell voltage on the deep cycle battery with the engine off - just put the leads from the voltmeter down in the acid to check voltage - each should be about 2 volts - sometimes a new battery will have a weak or defective cell. Remember deep cycle batteries require a deep cycle charge for optimum charge.
Hope this helps!