There is nothing wrong with asking the readers of the club to make du’aa’ for a Muslim who is going through difficulties

The communal dhikr which the scholars have warned against
takes two well-known forms:

(i)Where all those present recite
a wird or dhikr in unison

(ii)Where the leader of the circle
says something, and those present repeat after him.

The kind of asking for du’aa’s that is mentioned in the
question does not come under this heading. When the Prophet (blessings and
peace of Allaah be upon him) had finished burying the deceased person, he
would stand over the grave and say: “Pray for forgiveness for your brother
and ask that he be made steadfast, for right now he is being questioned.”
Narrated by Abu Dawood (3221); classed as saheeh by al-Albaani in Saheeh
Abi Dawood. 

And it was narrated that Abu Hurayrah (may Allaah be pleased
with him) said: The Messenger of Allaah (blessings and peace of Allaah be
upon him) announced the death of the Negus, the ruler of Abyssinia, to us on
the day that he died, and he said: “Ask for forgiveness for your brother.” 
Narrated by al-Bukhaari (1263) and Muslim (951). 

Based on that, there does not seem to be anything wrong with
what the sisters are doing in this club; rather it is something that is
prescribed in sharee’ah because it is pointing the way to goodness and
helping one who is in need. 

The Prophet (blessings and peace of Allaah be upon him)
encouraged making du’aa’ for a Muslim in his absence. He said: There is no
Muslim who prays for his brother in his absence, but the angel says: And you
will have something similar.”

Narrated by Muslim (2732). 

And Allaah knows best.