Gemara

(Beraisa): When Tishah b'Av or Erev Tishah b'Av falls on Shabbos, one may eat and drink [at the Seudah Mafsekes, i.e. the meal before the fast] as much as he wants. He may have a banquet as elaborate as Shlomo ha'Melech used to.

R. Yosi: Don't you agree that when Tishah b'Av falls on Motza'ei Shabbos, one must stop eating [on Shabbos] while it is still day?!

Chachamim: We agree.

Rishonim

Rosh (Ta'anis 4:32): A Tosefta (Ta'anis 3:12) says that when Tishah b'Av falls on Shabbos, one does not refrain from anything. I.e. he may bathe, anoint and need not refrain from private matters (relations). Maharam says "my Rebbi (R. Yitzchak of Vina) forbids relations, like one who buried a relative during the festival. We postpone the Avelus until after the festival, but even so, private matters apply. The same applies when Tishah b'Av falls on Shabbos. Tish'ah b'Av is like Avelus. The Beis ha'Mikdash is worthy to be Mevatel one Onah (normal time of intimacy) a year for it. One could say that regarding private matters, an individual's Avelus is more stringent than Tish'ah b'Av. It would be proper to follow my Rebbi even if he were lenient, and all the more so because he is stringent."

Rosh: However, the Tosefta connotes that one does not refrain from anything. This is the custom.

Hagahos Maimoniyos (customs of Tish'ah b'Av, at the end of Hilchos Ta'anis): If it is Shabbos, he does not deviate at all [from his normal meal]. However, the custom is to deviate slightly regarding Shabbos clothing. To show some signs of Avelus, we do not change all the clothing like on a normal Shabbos.

Beis Yosef (DH Kasvu): The Mordechai says that the custom is not like this [to show some signs of Avelus]. On [Motza'ei] Shabbos we do not remove shoes until after Borchu, except for the Shali'ach Tzibur, who removes them beforehand, lest he get confused.

Hagahos Maimoniyos (ibid.): It is brought from Rashi that if Tish'ah b'Av is on [or the fast is postponed until] Sunday, before Eichah one blesses Borei Me'orei ha'Esh, but there is no Havdalah over a cup [of wine], because one may not taste the wine, and we do not give it to a child, lest he get used to this. Therefore, one does not say Havdalah until after the fast. Then, he says Havdalah over a cup. One who did not say Havdalah on Motza'ei Shabbos may say it until [the beginning of] Wednesday (i.e. Tuesday night - Pesachim 106a). Some say to bless on spices on Tish'ah b'Av night. I disagree. Our Rebbeyim did not do so.

Mordechai (Ta'anis 635): When Tish'ah b'Av is on Shabbos and the fast is postponed until Sunday, relations are forbidden on Shabbos, just like one who buried a relative during the festival. Private matters apply.

Mordechai (637): When Tishah b'Av or Erev Tishah b'Av falls on Shabbos, some do not eat meat and drink wine at the Seudah Mafsekes. They show signs of Avelus. R. Eliezer mi'Mitz was displeased. Chachamim taught that one eats meat and drinks wine!

Mordechai (638): When Tishah b'Av falls on Motza'ei Shabbos, some say that we do not say Havdalah. R. Shmuel of Bonbork would say Borei Me'orei ha'Esh aloud without a cup. He would not bless on spices, for that is pleasure. On Sunday night he would say Havdalah in the Beis ha'Keneses and on the table, Borei Pri ha'Gafen and ha'Mavdil Bein Kodesh l'Chol.

Mordechai (638): When Tishah b'Av falls on Shabbos, some do not eat meat at the Seudah Mafsekes, and do not drink wine on Shabbos. One may set his table like Shlomo's. It is not a Chiyuv. One may have three Shabbos meals before the Seudah Mafsekes.

Beis Yosef (DH Kasvu): The custom is like Maharam.

Tur (OC 552): Rav Sar Shalom and Avi ha'Ezri say that when Tishah b'Av falls on Shabbos and the fast is postponed until Sunday, one may eat meat and drink wine, but our custom is not to do so, due to the Churban. Avi ha'Ezri says that some do not eat meat or drink wine at the Seudah Mafsekes. One may set his table like Shlomo's. It is not a Chiyuv. One may have three Shabbos meals before the Seudah Mafsekes. I say that since he refrains for meat and wine due to Avelus, it is forbidden. It is clear from Mo'ed Katan that whatever is evident that it is due to Avelus is forbidden on Shabbos. The Rosh used to eat meat and drink wine.

Beis Yosef (DH v'Chen): Also Semak brings from a Gaon that some do not eat meat and drink wine. However, he says that some say not to be stringent, for he disgraces Kevod Shabbos. It was taught about the Seudah Mafsekes that one may set the table like Shlomo. However, one must stop eating during the day, like when it is on a weekday.

Poskim

Shulchan Aruch (OC 552:10): When Tishah b'Av is on Sunday, or it is on Shabbos and the fast is postponed until Sunday, one may eat meat and drink wine at the meal before the fast, and sets his table with food as elaborately as Shlomo ha'Melech in his kingship.

Taz (3): Maharshal says that on Tish'ah b'Av we have no Avelus at all, except for the custom regarding clothing, that we change only the shirt, for Oneg Shabbos.

Magen Avraham (13): One may not refrain from meat. Even though there is no Chiyuv to eat meat on Shabbos, since he refrains due to Avelus, it is forbidden. This is difficult, for the Rema (YD 341:5) says that an Onen eats meat on Shabbos if he wants. I answer that the reason an Onen does not eat meat is not due to Avelus, rather, due to honor of the Mes. See Beis Yosef (OC 71, citing the Yerushalmi).

Magen Avraham (14): In any case, he sits brokenhearted, and does not conduct with Simchah. Therefore, he should not eat with friends. If there is a Bris Milah on Shabbos, he eats the Seudah before Minchah.

Mishnah Berurah (23): Bechor Shor disagrees. He says that if one normally eats with friends, and refrains on this Shabbos, this is like public Avelus. All permit to eat with one's family and bless with a Zimun, since it is Shabbos.

Rema: However, one must stop eating during the day.

Mishnah Berurah (24): One must finish eating before sunset. It is good to publicize this to the masses, lest they err and think that it is like other Shabbosos.

Shulchan Aruch (554:19): If Tish'ah b'Av falls on Shabbos, all of these matters [normally forbidden on Tish'ah b'Av] are permitted, even relations.

Rema: Some forbid relations, and this is our custom.

Taz (9): The latter opinion holds that this is like one who buried a relative during the festival. If so, also washing hands in hot water is forbidden, for also this is called private matters.

Kaf ha'Chayim (86): Nehar Shalom says that even the stringent opinion forbids only relations. Sefardim follow the Mechaber.

Magen Avraham (20): The Gabai announces that private matters apply. If this is Leil Tevilah (her first opportunity to immerse after being Nidah), she immerses and has relations. We rely on the first opinion.

Sha'ar ha'Tziyun (45): Halachah Berurah (7) questions announcing this, so one need not do so where this is not the custom, especially nowadays, that scoffers are common.

Mishnah Berurah (40): Some are stringent even for Leil Tevilah. Chayei Adam says that the Rema says that the custom is to forbid, i.e. when there is no Mitzvah of Onah, but not if it is Leil Tevilah. It seems that the Gra agrees. Therefore, one may be lenient for Leil Tevilah.

Sha'ar ha'Tziyun (46, citing Nishmas Adam): Similarly, we are lenient for one who returned home from a journey, for his wife desires him them, and also this is Mitzvas Onah. Everything is according to the person.

Kaf ha'Chayim (89): Surely, if a young man has lust, and refraining will lead to an emission, he relies on the first opinion. Being stringent will lead a leniency (i.e. a worse transgression)!