They do them at the Grand Floridian I believe and Saratoga. The waiting area in GF spa however is single sex whereas Saratoga is mixed so I would recommend that one.
Saratoga Springs you get a Couples relaxation package which includes an Aromatherapy and a Hydro massage with tea for two between in for $400.
Grand Floridian offers a Grand Romantic Couples Massage (50 mins or 80 mins) for $275/375 or an Instructional 3 hour session for $300
Mandarin Spa at the Dolphin hotel offers a Time for 2 80min massage which is $300
I haven't done any of these particular packages but Grand Floridian and Saratoga are nice.