I'm getting a bantam soon. I'm not sure what breed, but I think it will be all black. Will they lay colored eggs?
If you are getting a random bantam it is very slim you are getting an EE. Most bantam breeds lay white or brown eggs. It just depends on the breed and genetics.
An Easter Egger is a chicken that has been crossed with an Ameraucana, Araucana, Cream Legbar or some other blue egg laying breed somewhere down the line. They are crosses, not pure (or even an official breed in some cases). Appearance varies quite a bit but most commonly have muffs, olive legs, and pea combs. Others have single combs, crests, yellow legs, and any other chicken feature. They also come in almost every chicken color there is. Egg colors vary from blues, to greens, to pinks, to reds, to browns. Egg colors do not come from some special feed, housing, or anything else. It all depends on the genetics. Chickens will lay the same color egg its entire life (shade my change over time).
If you want colored eggs (blue/green), you'd need to get an actual Easter Egger, Ameraucana, Cream Legabar, etc. or a hatchery hybrid (Olive Eggers, Prairie Bluebell, Starlight Green Egger, Sapphire Olive Egger, Favaucana, Super Blue etc.). Marans (Black Copper) and Welsummers are known for laying dark brown/reddish eggs. If you are looking for a colored egg bantam, I know MyPetChicken has bantam EEs.