Question:
Can one say Tehillim after chatzos on Tisha B’av?
Answer:
It is controversial. Some poskim allow it, but the minhag is not to. If it is for a sick person, then it is permitted.
Best wishes
Sources:
M:B Shar Hatzion 554-8, Rivivos Efrayim 3-268, Mbais Levi 13 pg. 45, Divrei Malkiel 6-9-1, The Three Weeks pg. 135.