Zerex (Valvoline) has their version of FL-22 coolant, called Asian Vehicle Antifreeze. Apparently it's made in 2 colors, red and blue, but they're otherwise chemically identical and are compatible. Don't judge coolant only by its color because the color is mostly from dye, and without dye coolant is a very light clear yellow. Mazda's own version of FL-22 is green but is compatible with blue and red Zerex Asian Vehicle Antifreeze.
Mazda has a technical bulletin about the 2 types of coolant it uses:
http://www.miata.net/garage/tsb/01-033-07-1830b.pdf Notice it says you can mix the longer life FL-22 with Mazda's green coolant, but not with its orange coolant, which will turn black. I don't know how thoroughly any orange coolant has to be cleaned out before it's safe to put in FL-22.