The reference 2gb boards usually unlock easy with dual bios switch. i've heard the best one (most likely to unlock) is the Saphire toxic 6950 2gb, but i haven't seen those in quite a while.
really though, any of them can possibly unlock as long as the BIOS is not write protected. even if it doesn't unlock, the 6950 is pretty good overclocker and with a slight voltage tweak to 6970 settings you can usually reach 6970 speeds without unlocking shaders.
on a budget and can only affort the 6950 but want to see about unlocking without any problems like artifacts
This is something that obviously isn't guaranteed and is no longer really likely with any of the models available now. The reference cards were the ones that readily unlocked.
The best answer for this question is, find the least expensive HD 6950 2GB that has a dual BIOS switch. A lot of the earlier models had this feature but not so many anymore. Without the dual BIOS you could brick your card. Read reviews on newegg or elsewhere to make sure, alot of manufacturers have gone the bait and switch route, selling a card that looks reference or unlocked but has been replaced by a card w/o dual BIOS.
Its unfortunate but the unlocking was something that was really available 6 months ago, but now you had better appreciate the card for what it is first.
I have heard that msi has a BIOS that can unlock the TFII and TFIII cards, I think that's the best shot at unlocking currently.
Just a heads up, the 1 GB models unlock too, without a dual bios switch i'd suggest having an extra card handy incase you have a bad flash you can boot with the extra card, and reflash the 6950 back to stock. To unlock on the 1GB models you don't flash the 6970 bios like the 2gb models, instead you edit the stock bios to unlock shaders, if successful you can from there test voltage and clocks in windows at 6970 settings. If stable you can add those to the bios the same way.