Is it permissible to consistently recite specific supplications during morning and evening remembrances?

There is no impediment to a Muslim supplicating with a specific prayer for himself and for others at any time, due to the generality of the Prophet's (peace and blessings be upon him) saying: "Let each of you choose the supplication most pleasing to him, and then supplicate to Allah, the Almighty, the Majestic."