First of all, you will need to estimate the number of diapers and covers to bring on your trip. Keep track of the number of diaper changes you make in a typical day. Then, decide whether you would like to bring enough diapers to last the whole trip or if you'd rather bring fewer diapers and wash them along the way. Always throw in a few extra diapers and covers to make sure your bases are covered. Be sure you bring your trustiest diapers along to avoid the hassle of leaky diapers on the road. If you use cloth wipes estimate the amount you'll need to bring and fill a large bottle with your wetting solution.
Don't forget your detergent and other laundry necessities if you are planning to wash the diapers during your trip. It's a good idea to bring a roll of quarters or two if you'll likely do laundry at a hotel or laundry-mat.
A waterproof tote or wetbag is essential for storing used diapers. Be sure the bag is fully waterproof so you'll be free of leaks. Always remove solid waste from a diaper as soon as possible - and before storing with the other diapers in the wetbag. Bring some plastic bags for storing soiled diapers until you can find a restroom for proper disposal of the contents.
The supplies listed above can all be stored together in a small suitcase, duffel bag, or laundry basket. Be neat and tidy when you pack so your supplies can be transported together whenever you need to change a diaper, whether at a rest stop or your destination.