bulldogs and children's medicine

my english bulldog was treated for pneumonia for nearly the first year of his life. after a year of treatment, he stopped exhibiting the extreme symptoms he had during the illness, but he still deals with a runny nose on a daily basis. he is now four and i have seen two different vets in an attempt to rid him of this last symptom with no impact. i even tried feeding him a very small amount of children's benadryl each day which also had no impact. at this point, i have stopped trying and have learned to coexist with the snot. any suggestions?