Outside of very specialized services, renting game consoles is not really a thing here, no.
Even if you could find a way, I would strongly consider you to reconsider this plan. You're free to parent as you see fit, of course, but giving a child a birthday "present" that will then immediately be confiscated / taken away from him forever the very next day does not sound like a way to make a child happy, nor does it seem particularly effective for teaching some kind of lesson.
Maybe just take the simpler route of giving him a different present that you would be happy for him to keep, and/or taking him somewhere special (where unlike a present, the expectation from the beginning would not be that he could go there every single day).