If you are looking for a domain registrar which would allow you to register or buy domains with an unverified PayPal, then these two sites is what I'd recommend : Name.com or Namcheap.com. This domain itself was bought from Name with an unverified PayPal account.
I have been very fond of Name since the time I registered my first domain. Their support, response time and everything about them is fantastic. You never have to wait on Name for any support or response like you might do on other registrars, because they are fast, really really fast. I have had no complains about Name at all; their interface is so cool, the domain registration is always extremely fast even with an unverified paypal and their support is guaranteed to satisfy you.
I have had no previous experience with Namecheap because as said above, Name was the only domain registrar that I had used. I had read around the web that Namecheap too accepts unverified Paypal, but I never thought of giving it a try, since I was all satisfied with what Name had to offer. But, a day came when Namecheap had the best domain registration offer ever, and I could not resist it! Namecheap was giving away domains for 0.99$ (24 hours offer). So, it was the perfect time to test out something like this, to get to learn whether it accepted unverified PayPal or not, and finally, the answer is : Yes, it does.
I cannot say much about Namecheap because I have not really tried their service for long enough. I do not run into trouble with my domains frequently, so I haven't got to test how their support or response time is, but it's all around the web that they are one of the best domain registrars. I have seen plenty of people recommending them. In fact, if you ask for recommendations on a discussion forum, most of the members will put their name first.
That's two of the registrars that I have used so far, and by the looks of it, I don't think I'll ever need to move to a new one. Both of them accept unverified PayPal for domain registration and the transaction is almost instant; you don't need to wait to get the domain registered. You can Google for the coupon codes of both the sites to get discount on the price of the domain. If you are going to use Name.com, use the code PRIVACYPLEASE to get free who is protection (you can extend the protection for as long as you want). Namecheap provides free who is protection on every domain purchase, so you don't need to enter any coupon code.