Is it permissible to encourage children to pray by giving them money, and will this method be fruitful?

There is no legal impediment to encouraging children to pray and the like, whatever their age. This is indicated by the hadith (definition) of Al-Rubayyi' bint Mu'awwidh regarding the fasting of Ashura: "And we would make our young ones fast, and we would make for them a toy of wool. If one of them cried for food, we would give them that until it was time for Iftar (definition)." This is evidence of the permissibility of pleasing and entertaining children with things that encourage them to perform acts of obedience.