If I understand you correctly - you would put the water and container on the scale and zero it out. Then adding the coin would give you the same weight as in air.
You need to weigh it hanging in water. The analytical scale I use (a 4 beam Ohaus balance) has a hook above the normal pan and a free arm that can support the water and container.
Here is a sketch I made of how it works using a picture of an Ohaus scale like mine. The arm in the Photo is in the balse - you just raise it to do the test.
Here is another set up I found on the internet - it will work but you would have to adjust your calculations for the effect of the wire.