Peer to peer rentals are a fad based on the faulty premise that the renter will take better care of the property because an individual owns it (not a faceless corporation). You will still be faced with all the aggravation and expense of having to fix the stuff the renters break. And the bike will no longer feel like it is "yours" anymore. It will have become a community bike. Kind of like the difference between having a wife or that girl you pick up, down at the honky tonk on Friday nights.
But if you look at your finances closely, unless you are still making loan payments on the "old" one, you may find that you can afford to own more than one bike. The insurance per unit tends to be cheaper when you have multiple bikes on the policy, softening that blow. Operating expenses (gas, oil, tires, etc.) tend to be split between the two since you really can't ride them both simultaneously (without someone else's help) anyway.
If you are still making payments on the first one then maybe you are just being a bit impatient. Wait until #1 is paid off and then go looking for #2.
If you really can't afford to have two bikes, buy the one you want the most and sell the other. It's that simple.
Like many others have already stated, I would lend mine to a trusted friend or even forum member I may not have even met before if the conditions were right. About 2 years ago a friend of mine who now lives in TX was back in PA after his fathers death and had to stay for a couple weeks until all of the estate affairs were handled. I gave him my Buell for almost 2 weeks and thought nothing of doing so. I'm fortunate at this point in life to own multiple bikes and don't always ride each of them as much as they should be ridden.
No rentals here. I'm not in that business and don't have the deep pockets I would need when your next-of-kin came after me in spite of any waivers you may have signed.
No renters, no borrows, and no, you can not through a leg over my bike!! That holds for my cars as well. No dogs throwing a leg over the tires as well!! If I need a vehicle when traveling I rent one. Others can do the same. I would rather rent one for a friend in need than lend out mine. I've learned over many years to avoid hassles and liabilities whenever possible.