I have found this method where you can buy bitcoin with paypal. The fees vary (around 15% to 25%) but it is instant.
Here is the method:
1. Go to https://www.weselldoges.com/limits and email them with their support email.
This should make your limit 15$.
http://wesellredd.com/ or http://weselldark.com/
also works.
2. After you can buy doge, buy doge, and have it sent to a dogecoin wallet.

3. Go to shapeshift.io and select Dogecoin -> Bitcoin

4. Deposit the doge to the address they give you