My question concerns the marriage between cousins. Could you please explain if this is acceptable?.

Rabbi Waldinberg in Tzitz Eliezer 15, 45; concludes after a lengthy discourse that although it is not prohibited according to Torah or rabbinic law, since contemporary research proved that the risk of deformed children is high is such case, such relations should be discouraged. I heard that Rav Shaul Yisraeli said the same even though he himself married his cousin.