When I clerked on the 11th, the only real deadline was getting shamed by other members of the court. GSA (I think, or it was administrative office of the federal courts) circulated a report showing how many cases each judge had and for how long (basically like an A/R aging schedule). My judge was strict about us turning around opinions. Barring some complication we were expected to have oral argument opinions drafted for circulation to the panel before we went to the next setting (which typically happened every six weeks or so).
He used to always say, "write fast."
/csb
After opinion is drafted it then depends on how quickly the other two panel members (or full court if en banc) take either to sign off on the opinion or draft concurrences or dissents. Average cases would have opinions issued around 90 days after oral argument, sometimes sooner, but usually around 3 months.