Praise be to Allah.
Firstly:
It is permissible to rent out part of the mosque for permissible purposes that are appropriate to the respectable status of the mosque, in order to raise funds to spend on the mosque, subject to two conditions:
1. That this part of the mosque is not needed for prayers;
2. That most of the congregation of the mosque agree to that.
This is based on the fact that it is permissible to manage the waqf (endowment) and change its design in ways that serve its interests.
Please see the answer to question no. 136146 .
Secondly:
Gathering to offer condolences in a house or tent is a matter that is disliked (makruh) and is contrary to the Sunnah, as has been explained previously in the answers to questions no. 14396 and 82183.
Based on that, it is not permissible to set up a tent in part of the mosque or in its courtyard for offering condolences, whether that is for rent or not.
And Allah knows best.
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