Answer:
Avenged Sevenfold is probably the biggest name they've ever opened for, but they only did that for one show at Edgefest in Little Rock, AR. They've opened for Stone Sour and Theory of a Deadman on the Avalanche Tour.
On their Christian music side, though, they're pretty much as big as it gets, so most bands have to open for them. The only exception I know of is they opened for tobymac for a few shows.