This paper presents the theoretical study of couplestress effect on the squeeze film lubrication of cosine form of convex curved plates in which the upper plate has rough structure and lower plate is with porosity in the presence of an externally applied magnetic field .The gap between the plates is filled with non-Newtonian conducting lubricant of film thickness which consists of nominal smooth and rough part. The modified Reynold’s equation is derived using Christensen’s stochastic theory for rough surfaces. Expressions for dimensionless pressure distribution, load carrying capacity and squeeze film time are derived. The solution of the modified Reynold’s equation is obtained and for various physical parameters the results are discussed in terms of squeeze film characteristics of the bearings and graphs are plotted for the results. It is seen that for couplestresses in the presence of transverse magnetic field surface roughness effects are more prominent as compared to non-conducting Newtonian fluid(NCNF) in case of cosine form of convex curved plates. Tabulated values shows, for increased values of couplestress parameter, magnetic and roughness parameter load capacity and squeeze film time increases in transverse roughness case and these quantities decreases in case of longitudinal roughness and also decrease in load carrying capacity and response time is seen in case of permeability compared to impermeable case.