I probably would not use "could" in this case, "will" feels more natural to me.
Here is an interesting discussion on the modals.
I prayed to God that I could make a lot of friends all over the world.
I prayed to God, requesting that I could make a lot of friends all over the world.
Is the first sentence fine, or should I add 'requesting' as shown in the second sentence?
'Requesting' is not necessary.
I see nothing wrong with 'could'. 'Would' is also fine. 'Will' is not always possible in this sentence, which begins with the past-tense form 'prayed'.