This situation is kind of weird. Most 135 Ops specs give specific requirements for using an airport as a legal (Flight Plan) alternate however, to my knowledge, there is usually no mast list of airports one may use. You should be able to use any airport in the country that meets the Ops Spec Requirements.
Example Ops Spec;
May use the following mins for filing an airport as an alt...
Take the lowest authorized (No "NA" in alt mins section for that IAP) IAP to the airport desired and... (400:1 Rule)
-Add 400ft to lowest HAT/HAA
-Add 1 SM to lowest Visibility
EX) ILS with 200ft and 1/2 mile mins. In order to file this airport as an alternate, the wx must be at least 600ft and 1 1/2SM.