I am a Coumadin clinic nurse in our local hospital Anticoagulation clinic. I also have arthritis myself and I understand your frustration.
I think that there should be other alternatives out there for you. It may depend on what kind of arthritis you have and why you were placed on the Coumadin. Will it be long term or short term terapy?
I would seek out a Coumadin clinic in your area sometimes called an "ATC clinic"- they are mostly run out of larger hospitals. They are trained in managing Coumadin therapy and special situations like yours. Pharmacists and nurses work under the direction of a doctor but are more proactive in your care and take time to figure out the best treatment plan for you. I would also not give up in trying to find a doctor for a second opinion a rheumatologist or cardiologist if the reason for Coumadin is heart related. Don't give up. I myself have been through 3 orthopaedics, 2 rheumatology and other family practice doctors just to get a diagnosis of arthritis- took a few years to finally find the right doctor who is willing to give you your options and weigh the risks of medications and side effects. I would keep exploring your options and eventually you will know when you find the right one.

Try Trigger Point Therapy - plenty of videos on Utube; self-help book by Claire Davis and self-massage Theracane from Amazon; or get a massage therapist who does TPT and also try the new nerve pain-removal theory of (PRRT) Primal Reflex Release Therapy -- and you may find much needed relief from pain without taking meds. Also wearing Yoga shoes and Yoga-toes to space out your toes and align your skeletal bones may help. You also may be allergic to wheat, gluten, night shade vegetables (like potatoes, tomatoes and peppers) and sugar, so get an allergy test too. Exercise helps strengthen bones and muscles to protect the joints.