Homax makes a hand operated sprayer that I've used for knock down texture and popcorn ceiling texture. Works well if the mud/texture is mixed to the right consistency. It needs to be able to flow "just right". The description of pancake batter or oatmeal just doesn't cut it. Some like it thick and some like it runny. If the product doesn't flow to the sprayer, it needs to be thinner. If the product runs down the walls or drips from the ceiling, it needs to be thicker. Experiment. You'll want to try it on a scrap piece anyway.
There is also the hopper style sprayer that attaches to an air compressor. This is cheaper, assuming you already own an air compressor. Mud/texture consistency is the same as above. This unit will let you cover a lot more area for the effort. 20 square feet is about all I prefer with the hand held unit (the one with a gallon sized hopper).
Now that I think about it, mud consistency of store-bought applesauce is close to what you want.