With a clearer picture of the risks your offspring might face, a counselor can help you reach a decision that makes sense for you, your partner, and if you choose to go down that path, your children as well.
You can learn more about genetic counseling by visiting the March of Dimes Birth Defects Foundation.
And if a man shall take his sister, his father's daughter, or his mother's daughter, and see her nakedness, and she see his nakedness; it is a wicked thing; and they shall be cut off in the sight of their people: he hath uncovered his sister's nakedness; he shall bear his iniquity. They include father, mother, step-mother, sister, step-sister, grandchildren, aunt, uncle, daughter in law, and sister in law.
Technically, this does not prohibit marriage to cousins.
I can't find anything in the Bible about this subject, but we are taught that it is not right to date your family.