If you don't have time to wash your coils and/or more then one, you could try what I am doing mostly, when in that situation. If you have clearer juices and most of them are fruit or candy flavored, unscrew the tank, open it, remove the coil and wash out the tank or at least clean it with qtips. Then grab the coil, close/cover the airhole and blow into the coil from the top, repeat 5-6 times till no juice comes out of the cotton anymore, prime it with the new one, put tank back together, fill it, let it sit for a bit, then use it.
However that doesn't work great with lower VG juices, or general tobacco/menthol flavors or as mentioned above heavy coffee or drink flavors. These will just mix with the other and kinda linger in the cotton till you soak them in water. Also it won't work if your juices have different VG/PG or nic content than the ones used prior, but other then that, its a quick fix if you can't clean your coils that moment or don't want them to mix with another.