Try Trafford Cars (phone 0161 928 1111). We use them regularly from Altrincham.

Or there's the number 18 bus. Turn right as you leave the entrance to the Marriott on Hale Road and the bus stop is few yards away near the junction with Brooks Drive. For most of the day the buses run at about 05 minues and 35 minutes past the hour and it's under 10 minutes to the airport.