How big is the OD of the tires? A large tire warehouse I worked for would use carton/bale clamp attachments on forklifts for up to about 6' diameter tires and then they had a special clamp type attachment with special "tire forks" on it for up to about 8' diameter. The forks were smooth triangular shape and they would open them up to fit around the tire, close them just enough to hold the tire under it's bottom side and lift it on or off a stack. They used 6000 cap. forklifts for the tire clamp fork attachments that handled the bigger tires.