I am a chaplain working in palliative services. I have to document my visits and I am always searching for the right vocabulary that can accurately describe each patient's particular beliefs and spiritual and/or emotional circumstances. I often encounter people who believe that God will consistently grant their wishes if they only have enough faith. I would like a word to describe that belief without making a judgment as to the accuracy or misconception of said belief.
If I understand your description correctly, the belief itself is called prosperity theology (among other names):
Prosperity theology (sometimes referred to as the prosperity gospel, the health and wealth gospel, the gospel of success, or seed faith) is a religious belief among some Charismatic Christians that financial blessing and physical well-being are always the will of God for them, and that faith, positive speech, and donations to religious causes will increase one's material wealth. ... Prosperity theology views the Bible as a contract between God and humans: if humans have faith in God, God will deliver security and prosperity.
If looking for a neutral way of describing the belief in a God that helps people, I'd use the word interventionist.
The person holds an interventionist view of the deity, trusting that a truly devout prayer will be answered.
Another way that this attitude towards God has been described is the belief in a personal God.
The person believes in a personal God, that God hears their prayers, and that by praying they are communing with God.