Kiddushin, Chapter Four, Mishnah Seven
This mishnah continues to discuss which descendents of converts may marry priests.
1) Rabbi Eliezer ben Jacob says: if an Israelite marries a female convert, his daughter is fit for the priesthood, and if a male convert marries the daughter of an Israelite, his daughter is fit for the priesthood. But if a male convert marries a female convert, his daughter is unfit for the priesthood. [The same law applies to] a convert as to freed slaves, even for ten generations, [his daughter is unfit] unless his mother is of Israelite stock.
2) Rabbi Yose says: even if a male convert marries a female convert, his daughter is fit for the priesthood.
Section one: At the end of yesterdays mishnah we learned that according to Rabbi Judah, the daughter of a male convert is unfit to marry a priest, even if the mother is an Israelite. Rabbi Eliezer ben Jacob goes one step further. As long as one of the parents is of Israelite lineage, the daughter may marry a priest. Only if both parents are converts is the female child forbidden from marrying a priest. The laws regarding the lineage of freed slaves are the same as those regarding converts. The daughter is unfit unless the mother, and also the father are of Israelite stock. [Note that the mishnah says his mother, but since we are referring to which daughters may marry priests, other versions read their mother. Also, although the mishnah only says mother it must also mean father, since even Rabbi Judah says that if the father is an Israelite, his daughter is fit to marry a priest.]
Section two: Rabbi Yoses opinion is that the only type of convert prohibited from marrying a priest is the convert herself. Children of converts, even if both parents are converts, are allowed to marry priests.