@Nate
I'll echo that it's a good idea to get a handle on why pressing makes your shoulder hurt. Specific structural damage/injury/wear and tear/inflammation and/or pressing form/mobility/shoulder mechanics can play a role.
As someone who is continuing to recover from shoulder surgery, I agree that ballistic overhead exercises, such as push presses and snatches, can be more shoulder-friendly than strict presses, but that also depends on the specific nature of your shoulder problem.
Whether substituting push presses in ROP is a good idea also depends on what you want out of the program. If you are specifically trying to increase your press, I agree with
@BrianCF that it probably isn't the best way. A lower volume press program would likely be more effective. If you can't press at all. or only very little, without pain, then a strict press goal is unrealistic to begin with.
If your goal is any combination of improving your push press, hypertrophy, maintaining a base of overhead strength for when you are physically able to return to pressing, and/or if you just enjoy lifting things overhead, then the substitution makes more sense.
BTW, I am a much bigger fan of push presses than jerks, especially if you have jacked up shoulders. For one thing, catching the weight in the lockout by dipping under it has a much greater mobility demand. If your shoulders are jacked up to begin with, chances are you don't have the necessary mobility/shoulder mechanics to do them safely. For the same reason, I'd recommend staying with a single bell. Doubles have a higher mobility demand, while singles give you more literal and figurative wiggle room to find a comfortable groove.
Edit: One more press variation to test out as a viable workaround is the seesaw MP. In my recovery from shoulder surgery this is the most shoulder-friendly press I've tried.
In a nutshell it's a double bell press where you start by pressing one bell while keeping the other in the rack, then alternate arms. Both arms work at the same time, but one goes up while the other goes down (hence the name).
Working both arms in opposite directions creates a counterbalance that allows for a very comfortable groove. And even though it's a double bell press, your shoulders aren't locked in to position like in a regular double MP. You have the same "wiggle room" as in a single press, but the second bell as counterbalance makes the groove feel even more stable. If you imagine pressing yourself away from the weight, having the counterweight facilitates doing it.