It's probably a side seal, which is a do-able DIY repair. I did it once, and IIRC the directions on
http://www.miata.net/garage/miata_differential.html are pretty good.
But before you do that, sometimes the leak is from the front seal (the pinion seal) and the oil just dribbles back and just *looks* like it's coming from the side seal. If it's a front seal then it's a much much bigger job.
So have a good poke around and make sure the front seal is good. If it's ok, then a side seal replacement is maybe a 1hr job if you have a set of stands and a good socket set...The Mazda seal is a just a glorified rubber ring and from memory was $35ea or something like that.