I have had a dry persistent cough for a few months now. No cold symptoms. Taken different antibiotics. Inhalers. Don't smoke. What can it be?

Not infection... A cough lasting this long is not likely to be due to infection, especially without fevers. Possible etiologies include bronchospasm from any cause, gerd, post-nasal drip or even a combination of these factors. See your doctor so this can be evaluated and treated.
Many things. Reflux, post nasal drip, undertreated asthma, chronic infection with mycobacteria, allergic bronchopulmonary aspergillosis, dust in your home/work environment, medications (including ace inhibitors), silent aspiration, neurogenic cough (rare), lung cancer (even in nonsmokers). Presumably the low hanging fruit (asthma, post nasal drip) have been addressed. See a pulmonologist.
See an allergist. An allergist might be more appropriate. You may have allergies and he will be able to test you and find out what you are allergic to.
See someone medical. Anyone who has a cough for two months has something wrong. It could be as minor as postnasal drip or as serious as lung cancer. But you would have to be seen and examined, and probably have at least an x ray to help decide. Did you see a doctor for the antibiotics? Are you on any other medications like lisinopril? Look up the side effects. Glad you don't smoke---stay away from people who do!