Flat, horizontal stone has been used as grave markers in Ireland in several places and certainly if you wander any reasonably old graveyard you will soon see the damage wrought by the Irish weather on the writing on a flat tablet or table. Mould isn't really an issue on stone, but lichen will colonise it eventually.
If you wanted something small and neat like the plaque but in stone, why not just ask a mason to do exactly that? A sloped writing surface with the memorial inscribed on the stone? There maybe limitations as to how small it can be made in stone though and a sloped surface would be far more subject to the wear and tear of Irish rain than a vertical one.