4 year old has acne like sores around mouth region for quite a while now. Have tried vaseline, coconut oil & polysporin (bacitracin and polymyxin). What is it & treatment?

See your DR. Throw away the polysporin (bacitracin and polymyxin) & see your dr.
He needs to be check. He is only two years old and you describe acne like sores, I will suggest the he be examined by his pediatrician and have the sores you describe as acne like examined and get properly treated, polysporin, (bacitracin and polymyxin) vaseline and coconut oil has not helped. So it is about time the child be examined for the proper diagnosis and treatment.
Have child checked. Could be impetigo. May need systemic antibiotics treatment.
Diagnosis first. Before treating any further, you need a diagnosis. Peri oral dermatitis, cold sores, impetigo, eczema... This could be many things. I would try to see a dermatologist who is comfortable seeing kids.
Oral antibiotic. He may need to take an oral antibiotic in conjunction with polysporin (bacitracin and polymyxin) to get rid of sores.