Hi Bob! Welcome to the Forum!
Firstly, the reason for the moss is because it is always in the shade, and never gets the sun or dries out, and moss loves that!
So there are a few organic ways of treating moss with out getting out the scary stuff!
1) Mix Dawn dish soap with water in a spray bottle and spray it. It may take several sprayings, but you will see it turning yellow and dying.
2) Mix bleach and water in a spray bottle and do the same.
3) Use a heat treatment like a weed torch
4) There is a product out called MossMax, put out by Bonide, that is a water based potassium soap spray, that again, you spray on the moss, and watch it die.
The moss will return though, as long as the conditions remain right, so if there is any way of making your driveway a little less shady, it would help.
Hope this helps Bob!