My son had cradle cap and I used a product by Seaside Naturals called Little Star Happy Halo and I would massage it into his scalp and then comb his hair and it cleared it up in about a week!
My daughter was not bathed at birth and I gave her her first bath at home 48 hours after birth, but she still developed cradle cap. I liberally applied coconut oil to her scalp and gently ran a fine-tooth baby comb through it. Worked wonders!