I see various sites which ask for donations which look to be for profit. When I looked at PayPal's website their donate button seems to be specific for non-profit organizations.
The reason I ask is I want to start some online websites which are educational and if people find them worthwhile, then they can contribute/donate money to me. I know I'll have to report the money as income, however I'm curious if there is an easy standard out there for receiving donations for profit.
I can't help you with your PayPal dilemma but there's something you should know: donations do not work.
You can't expect to make any significant amount of money through donations (i.e. voluntary payment where the payer doesn't get anything in return other than a good feeling).
This is based on my personal experience and experiences of many other people that I've read.
As to your question: PayPal does have something called donations for Personal Fundrasing (https://www.paypal.com/webapps/mpp/fundraising ) so if you can frame those donations as fundrasing towards keeping your website running, it might qualify. That being said, I can't find a clear explanation of what qualifies as "Personal Fundraising" so you probably would still run a risk of having your account closed by PayPal.
But it's mostly academic: even if people find your website useful, an astonishingly small number of people will donate. Based on my experience, we're talking 1 out of 10000 people.
If you think that you can create something unique that has some value to someone, it's much better to charge for it.
It's even better make money via ads (AdSense if it's a website with decent amount of traffic) than via donations.
you would basically do it like you would sell a product. Since there is no tax benefit, that's more or less what you are doing. Just make something saying donate here, or help support this site and link to a paypal sale form.