From: Rabbi Moshe Sofer
To: Rabbi Mordechai
For a definite milah shelo bizmanah, the Chasam Sofer rules stringently that it may not be performed on Yom Tov Sheni shel Galuyos, following the Rosh and Mechaber, supported by the Tashbetz's proof from Rashi that the principle extends to all Yom Tov Sheni. For a doubtful milah — where it is uncertain whether today is the eighth day — he rules leniently and permits it on Yom Tov Sheni, following the Noda BiYehudah, since a possible Torah-level obligation overrides the Rabbinic prohibition of the second day.
Source: Shu"t Chasam Sofer YD §250