nowadays when buying a chicken from Marnie it'll say "choose a coop for your new [color] chicken", so if it's not going to be a brown one, just cancel, choose chicken again, rinse and repeat until it says it's a brown chicken. Then in a few days you'll have your small brown egg.
This. If you want white and brown eggs, small and large, for the full shipment, this is how you do. When buying chickens for the first time, I always make sure to get one white and one brown. As quoted, she says which it is, so if she says white, then white? At the second white I do as described until I get the brown.
However, once I have my 1 small brown and 1 large brown egg (because you need 1 of those too), though? I immediately sell my brown chicken and go buy another white one to replace it. Then I make mayo or cook with brown eggs first until I have none left... because eventually I'll upgrade to all blue chickens (and eventually will add gold chickens too) and I want their eggs to stack with the ones I've saved up for when I need to do some cooking.
Oh, and something important to note? If you hatch chickens from eggs, the reverse is not true. Chicken color is determined randomly, just like when you go to buy them... but when hatching, you can't just back out. White or brown egg, you can get white, brown or blue (if you have them available) chickens. For that reason, I usually just buy my chickens and don't hatch any. I'll put any other egg into an incubator, but not a chicken egg.