Praise be to Allah.
It is permissible for a woman to colour her nails for the purpose of adornment, with materials that do not cause harm. And there is nothing wrong with her praying with that , unless it is a substance that prevents water from reaching what is beneath it, in which case wudu and ghusl are not valid unless it is removed. If the wudu is not valid, then the prayer is not valid.
It says in Fatawa al-Lajnah al-Daimah, 5/218:
And Allah knows best.