Coal will burn in a wood burning fireplace but to burn coal you need a grate for the coal for it to light and burn properly.
If your wood burning fireplace is just an open fireplace and not an wood burning stove fireplace insert then the heat from the coal will mostly go up the chimney and not result in much heat in the house.
But if the wood burning fireplace is a fireplace insert then as long as you have the grate for the coal to burn on then yes the coal can be burned in the wood burning fireplace insert.