The 2000-2010 PUMA crosswalk file located here will allow you to crosswalk between 2000 and 2010 PUMAs. As you will see, the PUMA10_Name lists counties included. You can also use this map to to see boundaries for 2000 and 2010 PUMAs as well as 2010 counties.
You may also find the forum response found here useful, as it links to files from the Census containing the relationship between 2010 PUMAs and 2010 counties.