Culling is selective removal from the flock, in this case, killing. In case of not wishing to cull, your flock should become "all in and all out," meaning you can't add birds unless they have been vaccinated because they will get it from the carriers. Some of the chickens can get better, some may get it again and again, but they will all carry it. Tylan can work on coryza, but if it isn't working I would switch to Albon or Di-Methox. Here is an link to read:
http://www.thepoultrysite.com/diseaseinfo/82/infectious-coryza