Question: I take regular medication and have managed successfully to fast on Yom Kippur by eating a small piece of cake and a shot of juice with my pills. What do I do on Tisha B’Av?
Answer: A Choleh She'ain Bo Sakanah is defined as one who is confined to bed as a result of their illness (See Shulchan Aruch and Rema OC 328:17). Only one who is considered this ill would be allowed to eat Shiurim (less than a Kezayis in a short amount of time) on Yom Kippur. The Mishna Berura (554:16) writes that Tisha B'Av is like any other Rabbinical fast whereby a Choleh She'ain Bo Sakanah should break their fast. In Biur Halacha (554:6), however he writes that if they can manage to eat in Shiurim on Tisha B'Av they have not technically broken their fast.
R' Dr. Avraham Avraham writes (Nishmat Avraham 4 OC 554:1) that only one who is eating to prevent becoming ill should utilise Shiurim. One who is ill should eat normally. Others, including the Aruch Hashulchan (OC 554:7) write that there is no concept of Shiurim on Tisha B'Av.
The custom is that one who isn't fasting should not receive an Aliyah on Tisha B'Av (Shulchan Aruch OC 566:6 and Mishna Berura 566:19). Following a personal incident when he had to eat, the Chasam Sofer (Teshuvos OC 157) writes that this Halacha doesn't apply on Tisha B'Av.
One who is not fasting omits Aneinu in his Amida (Biur Halacha 565:1) though should say Nachem if he says Birkas Hamazon (Rema OC 557:1).