You do not need to launder diaper covers after every diaper change. If it is damp inside, just air it out. Use the diaper covers in rotation: while one airs out, use the other, while another may be in the laundry. Usually the covers go into the laundry often enough due to soiling, but if not, launder them every couple of days.

If you are using a diaper cover that has Velcro closures, fasten the Velcro and turn the cover inside-out during laundering. This will keep the Velcro from catching onto other items in the laundry. Wash with the cloth diapers, hang dry. (As diaper covers are waterproof, and don't absorb moisture, they hang dry quickly.)