One may be tempted to say, that since these Tisha B’Av day camps helps the parents fast, running such a thing is a tremendous chesed, and perhaps the Magen Avraham who said that one won’t see any berachah is only talking about when there is no mitzvah. However, we will see that this doesn’t stand to be true.
The Shulchan Aruch (Hilchos Shabbos 306:5) mentions a machlokes regarding whether one is allowed to pay a chazon to daven on Shabbos. The Mishnah Berurah (s.k. 23) explains, that those who rule leniently maintain that in place of a mitzvah, Chazal never forbade one to take money for working on Shabbos. However, the Mishnah Berurah adds, that one won’t see any berachah from the money, like we find in Hilchos Rosh Hashanah (585:5) that if one takes money for blowing shofar on Rosh Hashanah or for being the chazon, he won’t see any berachah. (Even when it comes to cases of pikuach nefesh, for example doctors or midwives, there are poskim who say that no berachah will be seen from any money earnt. See Toras HaYoledes 58:1, who quotes the Shu”t Har Tzvi, Orach Chaim 1:204, and Shu”t Tzitz Eliezer 8:15:13.)
We see from the above, that even when carrying out a mitzvah, one still won’t see any berachah.