I realize that these types of tefilah are really minhag and not halacha, but maybe some halachic aspect can be found by you.
This year, is “Zidkascha Zedek” said on 17th Tamuz and/or 9th Av? Does it make a difference on when Mincha is being davened?
On the one hand, “tachanun” would not be said, but on the other hand an external note of sadness is being bought into Shabos by not saying it (hence my wondering if time is of any importance).
The general rule is that “tzidkascha tzedek” is not said whenever tachanun is not said.
Tisha Be’Av is called a mo’ed, and therefore tachanun is not recited — the same applying to “tziskascha tzedek.” This does not apply to the Seventeenth of Tamuz, when tachanun is said.