As already noted, they bred pretty well in captivity - although in the wild they seemed to require communal breeding populations when in a "boom phase", in captivity this would appear not to have been the case. Moreover, it is now believed that the species was naturally prone to population explosion and implosion, going through periods where it was no more populous than any other pigeon species and periods where it was exceptionally fecund, and that the European settlement of the Americas merely happens to have occurred throughout one of the latter periods. As such, the species was entirely capable of breeding well in smaller numbers - when the population decline happened naturally and at a more gradual rate.
There are a number of photographs of living Carolina Parakeet - they can be found in the rather interesting Lost Animals: Extinction and the Photographic Record (2003) by Errol Fuller. I think this book also contains images of living Passenger Pigeon beyond the one posted upthread , but cannot swear to it - I own a copy but don't have access to it right now.
I can confirm that Lost Animals: Extinction and the Photographic Record does contain other photographs of living passenger pigeons. In addition, the book Extinct Birds (Errol Fuller; 2000) reproduces the photograph of a passenger pigeon posted elsewhere in this thread; it also features photos of a passenger pigeon egg, nest and chick.
Found some more accurate info of the species at Artis / Amsterdam Zoo : the very first bird was obtained 1846.
