The "Prayer vs. Manifestation" issue is a fascinating one -- and I'm jumping the gun here by replying, having only just decided to buy AFL -- on the strength of reading quite a lot on this Forum. Very helpful! And great to know how many intelligent, thoughtful and morally concerned people there are contributing to it.
I can agree with quite a lot of the views already expressed here, but am surprised that no-one has contributed what I've understood -- from quite a few books on manifestation -- is a normal difference between prayer and other manifestation techniques.
Prayer is very often framed as a petition to some power (called God, the Universe or whatever) to deliver what's lacking: in focusing on lack, very often it's not answered. Most manifestation techniques take the opposite tack: of visualising/feeling oneself as already having whatever is wanted, and thanking the power (God/Universe) in advance -- as well as focusing generally on the abundance already in one's life. And, also, not minding if it's not delivered -- as if not, there must be some good reason for it: and more questions to be asked about "why not".
As one writer of many, Stuart Wilde is very good (and very funny) on this. I practised it one day walking along the street with no money in my pockets -- and was amazed at how much there was to be grateful for. It made me feel rich! And happy. And I also realised just how powerful this attitude is -- when there were probably lots of people walking around with money in their pockets and in the bank, noticing nothing around them while obsessing about how poor they were.
In the Bible it says somewhere "Ask and it shall be given" (also the title of a book by Esther and Jerry Hicks). There is nothing new under the sun: but like the a another aphorism, "it's not what you do but the way that you do it" that often counts for most.
There is also a very interesting book called "Symbol Therapy" by Ulli Springett, a Buddhist counsellor and psychotherapist who takes a more constructive view of the function of desire, than non-Buddhists often understand by a Buddhist view of it -- as something simply to be got rid of. But the desire to be rid of desire, is a desire in itself. . .
In these terms, desire is not something "bad", but something natural to any animal that wants to stay alive (let alone reproduce and raise offspring). Given the faculty of reflection, human beings have more complex desires, whose realisation may not always be good for us, or have unexpected and unwanted outcomes. So Ulli Springett's recommendation is always to add "for the benefit of all sentient beings" to the expression of any personal desire -- and to mean it.