Is it permissible to encourage children aged seven and eleven to perform prayers by giving them money, for I have found such a method fruitful?

All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.

Islam does not prohibit encouraging children, regardless of their age, to perform prayers and other acts of worship.

Ar-Rubayyi‘ bint Mu‘awwith narrated that they used to make their children fast and when they cried, from hunger, they would give them toys, until it was time to break the fast. [Al-Bukhari and Muslim]

This narration is a clear evidence for the permissibly of encouraging children to perform acts of worship.

Allaah Knows best.