There are those (Sephardim and Chassidim, I guess) who have the custom to recite Shir HaShirim on Friday, Erev Shabbat. Do they also recite it on a Friday when Yom Tov leads directly into Shabbat?
If not, is there a reason why?
In my congregation we recite. However, the Mahazor Imri Pi and Tefilat Yesharim skip it.
Otzar Dinim U'Minhagim brings several reasons for saying Shir HaShirim every Friday:
Except for the last reason (117 hours of judgment), all the reasons mentioned would seem to apply both on a regular Friday, and a Friday that was a Yom Tov.
According to the last reason, if a soul is also not judged on Yom Tov (as discussed here), it could perhaps be argued that Shir HaShirim need not be said, since there were not 117 hours of judgment time during that week.