You can use the Sig P-220 7 and 8 round mags that are factory. The only difference is the cutouts on the mag body, for the push button release.
These mags can be found on e-bay and Gunbroker's auction sites. I bought 4 Sig 7 rounders for about 35 dollars from a seller on e-bay and they work great.
I have a Browning BDA/Sig 220 just like yours. Excellent shooter, isn't it? I love mine - it is the most reliable 45ACP pistol I have ever owned and is deadly accurate. I really think that these early Sigs were better made than the new ones I have seen lately. I can work around the European heel mag release for the trade-off in overall quality.
I lucked out...I was searching for a Sig 220 when I stumbled upon my BDA. The small dealer said nobody wanted it, because of the heel release and he had it marked down 200 dollars below a CDNN pre-owned P-220. (funny, because the CDNN piece was nothing special and the minty BDa was a rare bird) Needless to say, the BDA went home with me and I have loved it ever since.
Hang onto that pistol, I have found these to be quite rare. Browning only imported these from 1977-1980...they're not all that common. They made them in 9mm, 45 and 38 Super. The 38 Super is really rare and used ones go for about 2,000 dollars. The 9mms and 45s are still not very common.
Check e-bay and gunbroker...you're bound to find someone selling P-220 factory mags.
Aftermarkets? Well, the only aftermarket pistol mags I half-way like are Wilson's 47Ds for the Colt 1911s. Other aftermarket mags have been a real roll of the dice to me and not worht it. Pro Mag and Mec Gar are in that bunch...the quality of most aftermarket mags is just too spotty.
- Brickboy240
PS: My BDA/Sig also embarrassed all three of my 1911s, including one highly modified Colt Combat Commander. Actually, the BDA out-shoots just about every 1911 I have ever owned!