The most reliable way to ship gold coins and other precious metals is not FedEx or UPS, but USPS. USPS Registered Mail insures up to $25.000 per package. You are sending collectibles and not gold coins or "money". Once the coins have been graded, they instantly become collectibles.
Granted it can take up to 21 days for them to deliver the package, but it will be fully insured if it gets lost.
Extra tip: Make sure you double or triple box it, in good boxes. Or even put it in a strong plastic container, then double box it.