Early on in BioShock Infinite, you are given the chance to choose a choker for Elizabeth: either a bird or a cage. It seems like a no-brainer - freedom vs. imprisonment - but remember that her prison guard is a giant Songbird (and a CAGE is her salvation).
Songbird, Songbird, see him fly/
Drop the children from the sky.
When the young ones misbehave/
Escorts children to their grave.
Never back-talk, never lie/
Or he'll drop you from the sky.
NECA did a great job with their BioShock line,
but they never had a chance to make the Songbird. There's just no way - he's huge! It's hard to get an accurate gauge of his size, since when he's close enough to the player for a comparison, he doesn't fully fit on the screen, but he can easily carry Elizabeth in one hand! So we're talking at least Balrog size, if not more.
While NECA may have been out of the Songbird game, Funko isn't. Their POP! Vinyl line already plays fast and loose with size and proportions, so why not take the opportunity to make a scaled-down birdy?
Songbird, figure #68 in the POP! Gaming subline, is one of the oversized 6" figures, towering a massive 2" over the average POP!. The sculpt does a nice job of simplifying the game design: the idea is that Songbird is made from heavy, stitched leather over a mechanically augmented human within - while the Big Daddies were based on old diving suits (befitting their underwater operations), Songbird is inspired by era-appropriate aviators. There are shallow wrinkles all over, and thick stitches holding the panels together. Braided cords raise over his shoulders, connecting his wings to his body.
The wings don't move, obviously - no POP!s have articulation, which is why Funko can get so many licenses that are otherwise
tied up at different companies ("statues" and "action figures" are two different product categories) - so they're permanently curved around his body. It's not really a way he's seen in the game, but to do anything else would have made Songbird too big to fit in the box. The wings are a lighter color than the rest of the body, though they do have an airbrushing near the top to suggest dirt. The steampunky gears that, in the game, allow the wings to flap have been molded here as well.
Instead of using any separate weapons, Songbird relies on his massive size for attacks. He wears three-clawed implements on each fist, and has talons on his toes. All that is probably to help him get a better grip when he comes to roost, but they definitely help him tear buildings apart, too. His fixtutes are painted a metallic color - whether that's brass, bronze, copper, or what is up to you.
Taking a cue from Rapture's Big Daddy program, Songbird's glass eyes change color based on his emotions: green when he's content, yellow when he's on guard, and red when he's enraged. They POP! doesn't do that, of course, so they just went with flat red discs for the eyes - you could easily repaint them if you wanted to. There are metal frames around the eyes, continuing the aesthetic of the design, and a pointed "beak" that is actually a respirator with a tube that's strapped to his chest.
There was a Songbird statue available with the limited collector's edition release of the game, but if you want an affordable toy, this is your only otion. Technically, no, it won't fit with your existing toys of Elizabeth and Booker, but it has the distinct advantage of existing. Don't think of it as a literal representation of Songbird, but more like Elizabeth's memory of him from when she was young and he seemed more like a companion than a captor.