To have any chance of getting a deduction for a theft loss, you must have a reasonable basis on which to base an estimate of the cost of the coin collection and its value at the time it was stolen. For example, if he made a point of giving you gifts of coins and each one cost him at least $200, and you know he has made at least 30 gifts over the years, then that would probably be a reasonable basis for estimating 30 x $200 = $6,000). And if you could reasonably estimate the percentage of increase in value over the years, that would possibly be a reasonable estimate of the value.
If you do have a reasonable basis for the estimates, you could take the deduction, based on that, and include an attachment to the return, explaining the basis for the estimate. By disclosing the method of estimate, the IRS may allow the deduction and they may not, but you would not be penalized for taking the deduction.