If he is part or mostly Buff Orpington, he carries genes for a light brown egg. Plus whatever color egg his pea-combed ancestor laid - anywhere from white to brown. So let's say light brown averaging it all out.
What color egg do your easter eggers lay? If he is bred to someone who lays blue or green eggs, there is a good probability that the offspring will lay greenish eggs (or at the least, maybe grey eggs). If your easter eggers are all related, and include some who lay brown or cream eggs, there is more of a probability that some of them don't carry the blue egg gene "O" at all, and some of your blue/green layers may only be heterozygous for it. If this is the case, your rooster may produce a few plain brown-egg laying daughters as well as shades of blue green, even when mated with a blue layer.
For sure, mating him to any of your easter eggers who already lay a cream or brown egg, is going to produce brown egg layers.
Hope this helps!