Is it permissible for a Muslim to make any supplication that comes to mind upon entering the mosque, if he forgets the traditional supplication?

A Muslim must be diligent in reciting the supplications and remembrances (dhikr) authentically established from the Prophet, peace and blessings be upon him, and should not replace them with others. Whoever employs a specific remembrance or supplication and recites it regularly in a manner resembling the Sunnah, while it is not so, has introduced an innovation (bid'ah). As for supplicating with whatever is easy to remember upon entering the mosque when the authentic supplication is forgotten, there is no harm in it, so long as one does not believe it to be Sunnah or consistently adhere to it as if it were an established practice.