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.