Coquaternions, introduced by Sir James Cockle in 1849, form a four dimensional real algebra generalizing complex numbers. In recent years one can observe an emerging interest among mathematicians and physicists on the study of these numbers. In this work we present a Mathematica package for implementing the algebra of coquaternions. This package provides the basic mathematical tools necessary for manipulating coquaternions and coquaternionic polynomials, reflecting, in its present form, the recent interests of the authors in the area.