sure you could tint your casting slip, but if you want replicable results then you should really start with a dry recipe. also because it's a casting slip full of deflocculants it can sometimes act weird when used as a surface/decorating slip. colorants are almost always added as percentage of dry weight, since your slip is already wet, you have no idea how much water content is inside and you will not be able to get the same colors if you were to mix up a second batch due to this unknown variable.
best thing to do is take a white slip recipe (non-casting slip) or engobe or whatever you want to call it, then tint it the same way you would a glaze. oxides usually maxing somewhere around 5-6% depending on color you want, mason stains need to be up around 10% to get the intended color.
basic white slip (pretty much full firing range):
25 Ball (OM-4)
25 Kaolin (EPK)
25 Feldspar (Custer)
colored slips, like underglazes, will always look best when used with a glaze over it