A hanging, tabletop, or portable diaper caddy is the best way to organize diapers. You can diapers them stacked neatly inside so that you can grab each one as you need it. This works especially well if you are diapering two babies at once. You can keep each size separated so that you don't get them mixed up in a rush. If you want a more permanent option, you can always mount a cute shelf or basket above the changing table. Keeping diapers stacked within arm's reach will keep you from having to bend down and grab diapers from under the table at every diaper change. You'll still want a caddy for changing diapers on a different floor or when you are out and about, though.  You can have boxes or bins in the closet, under the crib, or in another hidden location to refill each caddy as needed. Just keep these boxes labeled so that you know what size you have! Keep the smaller sizes on top so they are easier to access and keep any larger sizes for the future toward the back or bottom of the pile.