How do I resolve my fathers last verbal request?

If the request was made orally and no one was a witness and it was never written down than it becomes nearly impossible to enforce it. Your fathers estate including the coin collection will have to be divided as indicated in his last will and testament. If the matter has been probated than this issue should have been resolved during that process

Unfortunately at this point without some sort of evidence such as a written instrument regarding this wish your word that he made that statement does not suffice to enforce the division of the coins. Whomever the coins would be left to in the will is how they will be handled short of such a document