Even during good times these things were not easy to get. They come in batches like only once a year, and always seem to be not available for 3/4th of the year. My suggestion if you need one right now, just buy a complete rifle =)
You are pretty well screwed at this point for Armalite parts unless Armalite, 762SASS or DSG Arms has it in stock (which I can assure you none of them have complete BCGs available). The only other options are to put up WTB posts here on the Hide (and BARFCOM, etc.) and try to snag on that way. Also, keep your eyes peeled on the PX here and the EE on BARFCOM (as well as other sites) as they do come available from time to time. Here is an ad from yesterday on calguns with one for sale (price sucks, but beggars can't be choosers now can they?!?!)! WTS: New Armalite AR-10 .308 Bolt Carrier Group - Calguns.net
Finally, as previously suggested, you can hit up GunBroker, but be prepared for sticker shock as in the not too distant past, complete Armalite BCGs were fetching $500 or more. Finally, if you aren't in any big hurry, it may be best to just call Armalite and place an order. Your wait time is almost guaranteed to be somewhere between a month and more likely as long as a year.