Du'a for a mother's long life

اللَّهُمَّ أَمْدِدْ فِي عُمْرِ أُمِّي بِالصِّحَّةِ وَالْعَافِيَةِ فِي طَاعَتِكَ وَرِضَاكَ

Allahumma amdid fi 'umri ummi bis-sihhati wal-'afiyati fi ta'atika wa ridak

O Allah, extend my mother's life with health and well-being in Your obedience and pleasure.

A general supplication, not a narration from the Prophet (peace be upon him).