What is a mastercard alternative?

There is no REAL alternative to the cards in term of control from the same instance (that is the USA). Diners and American Express and Discover card are all USA owned companies, so the same rules would apply more or less with those card issuers as with Visa and Mastercard.
For a not so widely accepted alternative there is the Chinese CUP card.
There is also the Japanese JCB Card.
There is soon going to be the Russian National Payment Card System.
There may be a European alternative called EAPS or the Monnet Card.