I am in the same situation except both our mothers are related... I was so relieved to hear that the risks of child birth are not that much higher than non related couples. And about the moral side... well I just remind myself that its not a matter of what others think its really about how happy the two of you can make each other in marriage. Besides God does not say that it is bad to marry your cousin, so why would a second cousin be immoral?
good luck with your future together.... and don't let what others think keep you from being happy...
Genetic counseling may help you to put your risks in context. Everyone has the risk of having children with problems, but because cousins share the same close ancestors, it is slightly more likely that they might share a disease gene.
Second cousins are fifth degree relatives and are predicted to share 3.1% (1/32) of their genes. In contrast, first cousins are predicted to share 12.5 % (1/8) of their genes. The closer the biological relationship is between parents, the greater proportion of genes shared, and the greater the chance to have a child with birth defects.
The background risk that every couple faces of having children with birth defects is about 2-3%. Genetic counseling will help define this for you personally based on your family history and ethnic background.
There are no special tests for cousin couples. The same tests a genetic counselor would discuss with any couple thinking about having children based on family history and ethnicity is what you should expect. Having the same blood type as your cousin is not a concern.
You can find a genetic counselor in your area through the National Society of Genetic Counselors.