Part of the error could be that you are not taking into account the volume of the wire that supports the stone. Something to try: weigh the stone dry, then tie the thinest thread that you have (or hair) around the lump. Put a small cup of water (make sure that the cup of water will not exceed the capacity of the scale), zero the scale and dip the suspended stone in the water.
Possible sources of errors for this test include: resolution of the scales is insufficient (ideally you should be using something with a resolution of 0.01g); air being trapped on the wire; the capacity of the balance being exceeded (ie if the balance has a capacity of 50g, and the cup, water and frame weighs 48g prior to taring, putting a 5g stone in the water will likely exceed the capacity of the scale as the taring doesn’t extend the capacity of the scale); smaller stones will have a tendency to give greater errors; disolved solids in the water (ie salt) will throw off the result; this method is a bit of a fudge method.
Note that if you are doing the test properly (ie accrediated laboratory) the test would be undertaken in a density bottle with the test normally taking a couple of days to complete with multiple steps, some very expensive gear and very precise measurements.