Radio Paradise does internet radio right. And the way they pay for it, well, it basically demonstrates that the Public Patron model could work. From their support page:

Our plan is simple: we create the best station we possibly can, refrain from contaminating it with advertising, and then ask you to pay us what you think it’s worth. So far it seems to be working out nicely. We’re not likely to get rich this way, but that’s not our goal.
Here at RP we’re not just non-commercial. We’re anti-commercial. We feel that quality radio programming and advertising just cannot co-exist. We also choose to refrain from forcibly extracting money from you by charging subscription fees. We leave it up to you to decide what our service is worth to you.
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Your voluntary support enables us to devote all of our time and energy to making RP the best station possible – and pays for the bandwidth, equipment and services required to keep the station online, and for the rather substantial copyright royalties we are required to pay.
The amount of your contribution is up to you – based on your opinion of how much you enjoy RP & what you can afford. A number of listeners have adopted the “one hour’s wages per month” formula – some can afford to send even more than that (thanks!), others can afford only $5 per month.
We particularly appreciate automatic monthly, quarterly or annual support payments. The more regular ongoing support we receive in that fashion the less we have to bug you on the air. Please consider choosing that option on the support form.
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And, as always, we understand that contributing money is just not an option for some of you. That’s fine. All streams and services at RP are open to everyone, and we will do everything in our power to keep it that way.

Please check out their great website and their broadcast. And of course, check the wiki, especially the In the News section under External Links.