Footballocks.com has the 2010 NFL bye week schedule archived under their "Bye Weeks" tab; click on the tab in the middle of the page and then click on the "2010 Byes" button under the article header. The NFL website also has bye weeks listed in their schedule archive, along with the result of every game.
The NFL's schedule archive is found by clicking on the "Schedule" button at the top of Nfl.com's home page, and then using the season filter on the next page. The website does not provide an immediate list of a team's bye weeks, but it does say which teams are on bye during any given week at the top of that week's page. All teams have their bye week between weeks four and 10.
The 2010 week four byes were Dallas, Kansas City, Minnesota and Tampa Bay; the week five byes were Miami, New England, Pittsburgh and Seattle and the week six byes were Arizona, Buffalo, Carolina and Cincinnati. The week eight and nine byes each had six teams, with seven from the NFC and five from the AFC. Week seven featured Detroit, Houston, Indianapolis and the New York Jets, while week 10 rounded off with Green Bay, New Orleans, Oakland and San Diego.