Any solid material that has its density less than that of water (or a liquid) will float, though boat-shaped heavier material will float because of the reason explained in the Archimedes Principle. Pumice is well-known naturally occurring “rock”, which is solidified volcanic froth of silica-the vesicles are not interconnected, hence there is no “permeability” of water in it. This twin property of high porosity BUT nearly zero permeability lets it float on water.
Google search for pumice, which is common material for scrubbing of dirt from our body, especially the heels.
These days roughly boat-shaped marble “dishes” are also made that floats on water (don’t large ships made of iron float on water?- Archimedes Principle). Such deco-items are popular these days, used in many gardens, notably the hotels. Now even “floating Sphere
Fountains” too are available in market made of any of the deco-stones-marble or even granite” (again take help of Google search!).
So yes a stone CAN float, naturally made or human-made, with a “trick”…