Yes and No. Yes, you can buy used ones, but why? when yours is used already? That aside...
If you're looking for used...well junkyards etc... the only place that I know of that you can find TI specific BMW OEM armrests are at a dealer. So you're going to have to do some looking. Also check out BMW parts internet sites... you can email them and ask them if they have that part... they're basically glorified BMW junk yards. Also, Bavarian autosport offers an aftermarket option that utilizes your existing cupholders to make a removable armrest with a leather top. Go to:
www.bavarianautosport.com for the aftermarket (non-BMW) armrest... I believe it's made by LeatherZ (LeatherZ.com)
My no is for- why not keep it? You can just recondition it with Leatherique products or (somewhat) equivalent? Go to
www.Leatherique.com or
www.leatherrepairkits.com (second link might not be right)... with these kits you can make that armrest like new and in whatever color you want within reason.