We are installing the brazilian pecan 5/16" solid x 3 1/8" flooring in our living room. We also purchased 3/4" solid oak for the bedrooms. Is there a pneumatic nailer/stapler that can tackle both jobs or do we have to buy two different machines. Most all I see either is for 1/2" to 25/32" or 1/4" to 1/2".

Unfortunately your going to need two different guns.
For the 5/16", use a 18 or 20 gauge staple nailer.
For the 3/4" use a cleat nailer, or 15 gauge staple nailer.