As the developer behind one of the ad network SDKs included in countless iOS apps, I struggled finding a good solution to this problem. Spoiler: there isn't one.
The good news is, while there were often collisions on SBJson; pretty much all versions of the version are compatible. For a while, we would compile our static library without the SBJson objects, and ship the library and SBJson separately.
Recently we decided to create our own fork of SBJson, and switch to using our own prefix, which allowed us to embed it in our library, and not worry about what other libraries were doing.
Note: another tricky gotcha with static libraries for iOS: There is a bug in the linker, in that it will not import Objective-C categories from `.o` files unless there is another another symbol that is recognized, such as a class of C function. This has caused crashers and much headache.