Only ones near airport (if sun beds) is Hollywood Tans on Beach Road in Beach Plaza (the blue building with Burger King on the frnt) or Gold Salon (only 1 bed and 10 AED per minute).
If you are wanting beds try marhaba delas they had a hollywood tan voucher 10 sessions 250 AED (8 minutes per session).
Are there any tanning salons in Dubai - preferably near airport way?
Do you mean sunbeds or spray tans? If you mean subeds see below
There is one in the blue mall on Jumeriah Beach Road
One at JBR and one in the FF platinum building at Media City
I do not know of any near the airport.
Spray Tans
Try Roots in Mirdif and the one in Garhoud near Welcare ( Cannot remember name sorry)