Given that, and given that each coin itself will also have its own intrinsic bias, then again the solution is the simple one I've outlined many times before - use a von Neumann debiasing approach, but with the additional caveat that you should start each flip from the same position (i.e. heads face up). That way any bias in either the coin or your technique is completely eliminated and you will always end up with a completely random result.
the thing about that von neumann method is if the person rolling the dice knows they are using it then they also know that only the first flip matters. the 2nd flip never affects anything. except whether to use the result of the first flip or not. with all of that information in their head, they're not going to be flipping the first and second flips the same way. probably not.