Just found via Slickdeals:
http://disney.eprize.net/moviereward.../toystory1and2 (WARNING: This page only describes the offer. Click "Home" and log into DMR to take advantage of the offer.)
This is the more traditional Disney upgrade coupon: Log into DMR (join it if you haven't already), enter the UPC from a DVD (or this time, even VHS) copy of TS or TS2 as your "magic code", and get a $10 coupon.
UPCs from the most recent DVD editions:
TS 10th Anniversary Edition: 786936294507
TS2 2-Disc Special Edition: 786936294521
Ultimate Toy Box: 717951005816
UPCs for the VHS toy stories:
Toy story vhs 786936670332
Toy story 2 vhs 786936127683
The coupons are NOW LIVE. As with the $5 coupons, they are separate $10 coupons for TS and TS2; you need UPCs for both films to get links for both coupons. They have the same terms as the $5 coupons (except the expiration date is April 11), so if you buy both BDs you can use both coupons.
Though some have reported the Ultimate Toy Box UPC gets you both coupons, that is YMMV; someone else said they only got TS and not TS2. When you enter it, look for TWO banners on the "success" screen--one for TS, the other for TS2. If that doesn't happen, enter one of the TS2 UPCs above.