The 32-year-old Koppen fractured his left ankle late in the first half of New England's season-opening win in Miami.
The 25-year-old Pryor, who missed the final seven games of last season due to injury, suffered a shoulder injury in the first half of Sunday's win over the San Diego Chargers.
Initial reports suggested Koppen might be able to return later in the season, but with injuries already mounting and Dan Connolly appearing steady in Koppen's place in Week 2, the team might not have been able to wait to see if Koppen could return.
Meanwhile, cornerback Leigh Bodden is still working his way back after missing all of last season due to injury, and remains on the injury report with a hand injury, though he participated fully Wednesday.
Before Wednesday's addition of Adams, Antwaun Molden was the only other available corner. After being signed late in the preseason, Molden made enough of an impression to stick on the 53-man roster, but he has played a mere 32 defensive snaps over three seasons with the Houston Texans, according to snap numbers logged by analytical site Pro Football Focus.
Adams doesn't boast much more experience. A seventh-round pick (224th overall) of the San Francisco 49ers last year, Adams played only 76 total defensive snaps in eight games at cornerback during his rookie campaign.
Cohen has the potential to fill Pryor's shoes as a rusher in sub packages.
Cohen, who played in the final three games of the 2010 season for New England, could be thrust right back in the mix.
"I'm happy to be here, happy for the opportunity, and ready to get in the game plan for Buffalo," said Cohen.
Chris Forsberg covers the Patriots and Celtics for ESPNBoston.com.