Alternative Compensation is at least one of the terms of art for how creative types can arrange to get paid for their creative works, apart from copyright enforced mechanisms.
How, specifically, can a photographer get compensated for doing photography, in a world where copyright does not exist? Since in many areas of photography copyright does not exist in any effective fashion, we can look at the world as it exists today. There might be some other ideas rattling around as well, though.
Work for hire is pretty what most photographers who make money do anyways. You're hired to shoot the wedding, the engagement. You might even be hired to shoot photographs of local newsworthy events. Your technical skills, your equipment, and your time, are rented to the customer. This is essentially how plumbers and most other skilled laborers operate. It's how I work, even though I produce copyrighted materials for a living. My employer pays me for my labor, and my employer enjoys the copyright protection on the fruits of that labor.
This is how the world works now. Wedding photographs and the like get copied and passed around to anybody who has the slightest interest in possessing a copy, despite copyright law. Copyright law is, for almost all intents and purposes (but not quite - there are rare exceptions) absent here.
Musicians are allegedly returning to performance as a primary money maker. Rather than relying on copyright law to protect the revenue stream from easily reproduced digital songs (which revenue stream mostly doesn't go to the musicians anyways) they are providing the consumer with an experience. They provide an entertaining live show. They also sell schwag, shirts and whatnot. This leads us to:
There's always a market for things, objects. Unique objects are better, but objects with any kind of perceived value can be sold for money. Ordinary photographic prints have very little perceived value, but there are other related objects.
So you can, at least, provide experiences and objects. Interestingly, we see experiences already being offered.
The photobooth, a computer set up with a webcam or a better camera, and some software, is increasingly an entertainment provided at events. The event photographer is perhaps uniquely positioned to offer this, and to sift through the results. This provides both an experience, an entertainment within the larger event, and a collection of pictures.
The currently-popular "trash the dress" event is another photographically themed entertainment, which can be orchestrated by the photographer.
As for objects, the standard photographic print used to be the object provided by the professional photographer. A high quality print was viewed as a valuable object in its own right. This is simply no longer true. Given a digital image I can have any number of prints at any number of sizes and qualities made for me for any price I care to pay. A photographer providing this to me strikes me purely as a way for the photographer to clip off a piece of the action, when I can place an order with a couple of clicks of the mouse.
There are processes such as tintypes and Ambrotypes which produce unique objects. These are indeed making a little bit of a comeback in the portrait market, mostly aimed at monied hipsters. There might be a market for an add-on to the usual wedding package, here, as well.
It's not clear to me what else there is, but if I was a wedding photographer I'd be thinking furiously about what kinds experiences and objects I could be featuring as add-ons to the basic wedding package.