The influence of grain constraint on the magnetic field levels required to complete the isothermal martensitic transformation in magnetic shape memory alloys has been demonstrated for a NiCoMnSn alloy, and the magnetocaloric performance of an optimally heat treated alloy was quantified. Ni45CoxMn45-xSn10 melt spun ribbons with x = 2, 4, 5, and 6 were characterized. The x = 5 sample was determined to exhibit the lowest transformation thermal hysteresis (7 K) and transformation temperature range during transformation from paramagnetic austenite to nonmagnetic martensite, as well as a large latent heat of transformation (45 J kg-1 K-1). For this composition, it was found that increasing the grain size to thickness ratio of the ribbons from 0.2 to 1.2, through select heat treatments, resulted in a decrease in the magnetic field required to induce the martensitic transformation by about 3 T due to the corresponding reduction in the martensitic transformation temperature range. This decrease in the field requirement ultimately led to a larger magnetocaloric entropy change achieved under relatively smaller magnetic field levels. The giant inverse magnetocaloric effect of the optimized alloy was measured and showed that up to 25 J kg-1 K-1 was generated by driving the martensitic transition with magnetic fields up to 7 T.