To
ensure good, consistent carbonation, we recommend you stay with the
recommended quantity of white granulated cane sugar. The priming sugar
is added for the sole purpose of creating carbonation, and the amount is not
enough to affect the flavor. Molasses, brown sugar and honey may
contain unfermentable sugars and contribute different sugar levels, and in
honey possible bug parts or hairs, which can adversely affect your
carbonation.
While you can experiment with them in your wort, we recommend you stay away from carbonating with them, or you may wind up with flat beer, gushers, or burst bottles.