There are no regulations prohibiting the transport of gold coins on airplanes.
The TSA recommends you inform a TSA Screening Supervisor prior to screening and advise them you are traveling with valuable coins. Request a screening in a private location. A witness will be required and can be a TSA Security Officer or one of your traveling companions. By requesting a private screening, you will be guaranteed that other travelers will not be made aware of the valuables in your possession.
If you are on an international flight and are transporting any currency valued at more than $9,999.99 USD, then you are required to inform the United States Customs Service. The report you will have to file is the "Report of International Transportation of Currency or Monetary Instruments, Customs Form 4790."
