Yes - most of those contain Tylosin - which is related to erythromycin. Personally, I would *not* give any animal (or human) a low dose antibiotic daily - for what is essentially a cosmetic issue (the staining). The reason is that these low dosages lend to creating antiobiotic resistant strains of bacteria - which puts entire populations at risk in the future. It could also be harmful, for example, if your dog developed an infection where they wanted to use an erthro-based medicine - but the medicine did not have much effect bc your dog had such a "tolerance" to it, based upon receiving the low-daily-dose. Hope that makes sense.
Sometimes, both tearing and staining is related to food allergies - so, maybe a look at diet may help - can I help there?