MAST is in POS - you can use coinking to mine other coins to autoconvert to MAST - if you do this you goto your coin wallets for the CK MP and tell it to convert to MAST. So yes, coinking can generate MAST but it can't mine them directly as none can do that.

At coinking select the Account tab - then wallets. For each set of MP mining types (Scrypy, SHA256d, X11, etc) select autoconvert all to your choice of coin. Some won't change from BTC but - even if the pool mined those any BTC would then be converted to MAST if you picked that.
*Edit to add explicit instructions for setting up CK to convert.