Binary magnetic alloys like Co-Pt are relevant for applications as components of magnetic exchange coupled composites. Numerous approaches exist to tune the coercive field of Co-Pt alloys primarily relying on high temperature processing aiming to realize chemically long-range ordered phases. The peculiarity of Co-Pt is that large coercive field and magnetic anisotropy can be achieved even in chemically disordered alloys relying on short-range order. Here, we study alloying of Co-Pt from bilayers of Pt(14 nm)/Co(13 nm) at temperatures up to 550°С, where bulk diffusion processes are suppressed and the dominant diffusion mechanism is grain boundary migration. We demonstrate that grain boundary diffusion mechanism can lead to the realization of a homogeneous yet chemically disordered Co56Pt44 alloy at temperatures of 500°С and higher. A pronounced increase of the coercive field for samples processed at temperatures higher than 400°С is attributed to short-range ordering. With this work, we pinpoint the grain boundary diffusion as the mechanism responsible not only for the homogenization of binary alloy films but also as a driving force for the realization of short-range order in Co-Pt. Our results motivate further research on grain boundary diffusion as a mechanism to realize chemically long-range ordered phases in Co-Pt alloys.