Given your edit, what I can best explain this material as is that you have a solid rock that works like a lighter-than-air gas. Yes, technically repels gravity, but the result is the same.
Therefore, your shipbuilding designs will be based in part around some lighter-than-air construction principles.
1: The 'lift stone' will need to be placed above the ship's center of mass. When something is in the air, it will naturally try to orient with the heaviest part facing down...so if your lift stone is below the center of mass, your ship will be unstable and likely to flip over, and get stuck that way.
2: For an extremely small, unmanned craft (like a buoy), a single lift stone will be enough to hold it up and keep it stable, however in an occupied craft, it will wobble around a single lift stone. Therefore, you will want multiple, smaller lift stones arranged around the edges of the ship, always equal in distance from the Center of Mass as the stone piece on the opposite side of the COM. So, for clarity, your Bow and Aft stones need to be the same distance from the COM, and the Port and Starboard stones will need to be the same. More stones will provide more stability in the ship.
3: Extra stability can be gained by placing stones on outriggers that extend beyond the body of the ship. But this raises a big problem.
4: Assuming that lift stone truly repulses gravity, you will need to make sure that it is kept very well secured at all times, and is only attached to the ship once construction is complete. This is because a gravity-repulsing stone would naturally eject itself from the planet if not held down. Likewise, a damaged ship that has lost a bunch of mass is going to have problems not simply ascending out of control, and the crew may have to cut loose some lift stones to regain control. For this reason, more small lift stones is better than a few big ones.
5: In combat, the primary target for warships will be the other ship's lift stones. All you have to do is destroy the casing around them, and they will hurl themselves into the sky, and eventually forcing the other skyship to fall.
As an alternative to 'gravity repulsive,' you could instead declare the stones to be extremely buoyant in atmosphere, This would cause them to naturally 'float' up to a certain altitude where their buoyancy is cancelled out by the thinness of the air. The closer they get to that altitude, the less lift they generate. In this case, recovering lost Lift Stones is difficult, but not impossible, and does explain why all the Lift Stones in the world haven't launched into space already.