Is there a homeopathic cure for trichomonas?

No. Trichomoniasis is a sexually transmitted disease caused by small parasites. Treatment with an antibiotic is the only proven effective treatment. It is important to get treated to protect yourself and your sexual partners.
Yes, collaboratively. Conventional treatment for trichomonas is normally very effective, and you would not be seeking homeopathic treatment. However, sometimes women continue having symptoms even after multiple rounds of conventional treatment. There are certainly remedies known to help vaginitis, and you need a professional homeopath to take your case in order to find your individualized homeopathic medicine.