I have tried most of the methods discussed here.
The acid tests and rubbing does cause damage - so I will use that only if the coin has been test cut or drilled.
The electric conductivity tester is easy to use but results are not always very accurate based on surface contaminants.
Measuring the weight - diameter and thickness is the method that banks and merchants used. Check
ebay for the old counterfeit scales. They are an area of collectables all by themselves. But the problem is accuracy when coins are out of round - say out of collar strikes or hammered coins. Weight and diameter alone is not too helpful since many forgers simply make their coins thicker.
The best I have found is Specific Gravity. You need a scale with a free arm above the balance pan so that you can weigh a coin in air and then in water. A good quality Ohaus scale is simple - it is a 4 beam balance scale and weighs very accurately to 0.01 gram (estimate to 0.0025 or so). There are on line tables to convert SG into various gold alloys. I test counterfeit coins for local coin dealers.
The best surface test is the XRF Xray Flourescence test. I have done that (when I can get access to the apparatus) and have had great results. It will detect all metals present to a few parts per million. The value of the test is highest when you are following trace metals as an indentifcation tool. Commercially the tests run $30 per coin or so, but if you make friends with technicians - it gets down to a couple meals and drinks. Some of the contaminants can be surprising.
Did you know that real silver coins made at the Zacatecas mint in the 1840s are contaminated with GOLD?