No
All combat damage is dealt at the same time, which means that the two creatures will die at the same time, and each one will add a trigger from Dark Prophecy to the stack. At the end of combat damage, the stack will look like this:
[Top of Stack]
Dark Prophecy Trigger
Dark Prophecy Trigger
[Bottom of Stack]
You can decide which order these triggers go on the stack (they're the same so in this case it doesn't really matter), but since they go on at the same time, you don't have a chance to cast Naturalize before they are both on the stack.
You are correct in your thinking that you can cast naturalize after one trigger resolves. However, this doesn't really do what you want: Even though Dark Prophesy is destroyed from Naturalize, any triggers that are still on the stack will still resolve as normal.
As a side note, if the card you draw from the first Dark Prophecy can be cast at instant speed, you can use it before the second Dark Prophecy trigger resolves. This could be useful if the card you draw is some kind of instant speed life gain, such as Crypt Incursion