Can A Couple With Blue And Green Eyes Have A Brown Eye Baby?

Yes. If the gene for brown eyes is present in one parent and it's on the dominant allele, the baby will have a 50% chance of having brown eyes. If it's on the recessive allele it will have a 50% chance again. If one parent has the brown eyed gene on the dominant allele and the other has the same, there will be a 75% chance. Same if one has it on the dominant and one on the recessive or if both have one on the recessive. So yes, it is possible.