Can you open the case? The reindeer motors I have seen have a TYC or TYC CW/CCW gear motor inside.
http://www.ebay.com/sch/i.html?_odkw=motor+tyc&_osacat=0&_from=R40&_trksid=p2045573.m570.l1313.TR0.TRC0.H0.Xgear+motor+tyc.TRS1&_nkw=gear+motor+tyc&_sacat=0
http://www.ebay.com/sch/i.html?_from=R40&_trksid=p2050601.m570.l1313.TR0.TRC0.H0.Xmotor+tyd.TRS0&_nkw=motor+tyd&_sacat=0
http://www.ebay.com/sch/i.html?_odkw=motor+tyc&_osacat=0&_from=R40&_trksid=p2045573.m570.l1313.TR0.TRC0.H0.Xgear+motor+tyc.TRS1&_nkw=gear+motor+tyc&_sacat=0
http://www.ebay.com/sch/i.html?_from=R40&_trksid=p2050601.m570.l1313.TR0.TRC0.H0.Xmotor+tyd.TRS0&_nkw=motor+tyd&_sacat=0