We present a study of granular Co-Pt multilayers by means of high-resolution transmission electron microscopy (HRTEM), extended x-ray absorption fine structure (EXAFS), SQUID-based magnetic measurements, anomalous Hall effect (AHE), and x-ray magnetic circular dichroism (XMCD). We describe these granular films as composed of particles with a pure cobalt core surrounded by an alloyed Co-Pt interface, embedded in a Pt matrix. The alloy between the Co and Pt in these granular films, prepared by room temperature sputter deposition, results from interdiffusion of the atoms. The presence of this alloy gives rise to a high perpendicular magnetic anisotropy (PMA) in the granular films, as consequence of the anisotropy of the orbital moment in the Co atoms in the alloy, and comparable to that of highly-ordered CoPt L10 alloy films. Their magnetic properties are those of ferromagnetically coupled particles, whose coupling is strongly temperature dependent: at low temperatures, the granular sample is ferromagnetic with a high coercive field; at intermediate temperatures the granular film behaves as an amorphous asperomagnet, with a coupling between the grains mediated by the polarized Pt, and at high temperatures, the sample has a superparamagnetic behavior. The coupling/decoupling between the grains in our Co-Pt granular films can be tailored by variation of the amount of Pt in the samples.