You have two limitations: rated current for inner conductor and that for connector.
If you can get the cross section of the inner conductor, then you can calculate/estimate it. Of course a third factor is the environmental temperature.
Connectors of the snap-in type where the electric contact is good can handle large currents. A bit of attention should be give to the junction conductor-pin, but being an assembly done at a factory ad not home made, is surely well assembled and robust.
If you need just an idea of which rating you should use to stay safe, you can think that 0.5A ca flow continuously and 1A should be also compatible. Thing e.g. of GPS applications: there are miniature cables and connectors, the GPS is supplied through them and a 500 mA current is not impossible under poor coverage conditions.
Of course my talk is not a accurate estimate, that is not possible without a lot of details that in the datasheet seem to be missing.