What is the ruling on saying: "May Allah give you the good tidings of the the face of the Prophet, upon him be peace and blessings" by analogy with the saying: "May Allah give you good tidings"?

There is no harm in the supplication "May Allah give you glad tidings of seeing the face of the Prophet, peace and blessings be upon him"; because it is equivalent to "May Allah give you glad tidings of Paradise," as seeing the Prophet, peace and blessings be upon him, is a necessary consequence of entering Paradise. The scope of supplication is wide.