These are the colors given by AC Roberts in his four-part series on the in Nautical Research Journal several years ago:
Kearsarge-1864
Hull-black
Bulwarks, plank shear, head rail molding-white
Decks, houses, hatches-natural
Waterways-blue
Guns and tracks-black
Masts-white
Yards-black
Boats
Hulls-white
Bilges and floors-blue
Gunwales-yellow
Thwarts-natural
He qualifies a couple of these selections. The choice of natural for the houses and hatches is based on other models of ships of this era and they could possibly have been painted white. The choice of blue for the waterways is based on contemporary receipts which showed the ship had received a quantity of blue paint.
I have always found his choice of white for the boats' hulls curious as some of the photos of the ship he uses to illustrate his articles seem to show that the boats were black during this time period.