The purpose of this study is to find out about the safety and effectiveness of the study drug, sirolimus, in patients with uveitis and to utilize the potential effectiveness of sirolimus, and yet to avoid the potential complications of systemic use of the drug. In this study, the investigators will administer sirolimus either around (subconjunctival injection) or inside the eye (intravitreal injection). Local administration of sirolimus to the eye is not expected to have effects on the rest of the body. Therefore, it may offer a safer way than the current methods used to control the inflammation caused by non-infectious uveitis.