Falsifiability is from a scientific viewpoint worthless anyway. Statistically, what you would put forward is a null hypothesis (the coin is fair) and an alternate one (it isn't). You would then compute a test statistic (in this case, the proportion of heads with respect to the number of flips) and see how likely that is under the assumption of the null hypothesis. The less likely, the more reasonable it is to reject the null hypothesis. This is the scientifically sound decision.
In fact, considering that most scientific research is statistical in nature, your example demonstrates why no scientist makes use of falsifiability in any profound way during his research. It would be totally useless, one would never arrive at scientific conclusions.