Generally speaking, someone requiring immunosuppression would be more susceptible to infections. Specifically, for the commonly used drug, Cyclosporine A, side effects can include; lowering of white blood cell count, nausea and loss of apetite, kidney malfunction leading to raised blood pressure and increased growth of bodily hair.

There is usually increased risk of infection including viral, bacterial and fungal infections. However, there is difference between autologous and allogeneic hematopoietic stem cell transplantation as far as transplant-related complications are concerned. . In allogeneic stem cell transplantation patients can develop graft-versus host disease (GVHD) and veno-occlusive disease (VOD), too. 

Do you know what cytokines are increased / decreased after implantation of your stem cells? This can give you a guidance on what IS to use. I guess you are using allogenic SCs... The most common IS used in uveitis is MTX and has significant adverse events apart from infections. I also guess you expect an innate immune response? Antigenicity should be in the list of studies you may want to do as well.

If your animal model shows signs of uveitis after transplantation I would be careful to go on in that direction. Animal models also give a false idea of immunogenicity when translated to human trials.