Hi, Mark,
The Stoeger coachgun is a fine CAS shotgun. My wife shoots one (double trigger) when she shoots the black powder categories in SASS. It was her first CAS gun, and it's still going strong after seven years. Stoeger was bought by Beretta several years ago, and there have been reports of parts being hard to get. I can't comment personally on that, as the only parts I've replaced on Lorelei's gun have been the firing pins, and I got the hardened firing pins from Long Hunter
http://www.longhunt.com/gunparts/gun_parts-sp.shtml.
As far as the single versus the double trigger, I favor the double trigger for Cowboy shoots because of simplicity. There is less to go wrong with that system. For bird hunting, the double trigger is actually a better choice, if you have different chokes in each barrel (the stock non-interchangeable choke on a Stoeger is Improved Cylinder in one barrel and Modified in the other). That lets you decide at the time of firing which choke you want to use; especially useful in bird hunting as you don't know how far the critter is going to flush. The single trigger lets you decide which barrel to fire first depending on a selector lever (which takes a fraction of a second longer to set if you have to change it), and the second barrel is then selected by the recoil of the shotgun.
I've never fired a Stoeger single trigger gun, but there are reports of other low-end single trigger doubles "doubleing", or firing both barrels at once. There are also reports of failure to reset with low-recoil loads. These have not been Stoegers, but other guns. I have yet to see a single-trigger Stoeger up close, or even talk to someone who owns one.
All that being said, Lorelei and I both use double trigger shotguns for CAS (mine is an external hammer TTN) and single trigger shotguns for skeet (Browning Citoris). I really don't find one any faster that the other, once you get used to either system.