Is it permissible to designate a specific day for a particular supplication, such as "Du'a of Thursday" or "Du'a of Friday Night"?

It is not permissible to designate a specific day for a specific supplication that has no basis in the Shariah, as this is considered an innovation (bid'ah). It is permissible to supplicate with any words that do not contradict the Shariah at any time. However, designating a day or a month for a particular supplication is an additive innovation. Many of the supplications designated for specific days are concocted by preachers. It is permissible to supplicate with them as long as they do not contradict the Shariah, but without designating a specific time for them without a Shariah-based evidence.