I believe they date from 1864 or 65 though it is a late date for the most part the 114th PA uniforms remained the same through the whole war. Even looking at various paintings that people like Don Troiani you can see they Differ from whats in game. More examples below this.
Don Troiani's 114th PA painting I am lucky enough to own the reproduction of the 114th PA jacket Don had made based off his original for the model to wear for this painting
Last but not least an original uniform with pants and fez can clearly see all the pictures and even original uniforms they were not wearing pataloons