We propose a new method for estimating differential rotation in binary stars, for which only moderate to poor phase coverage can be achieved (rotation period of order of a few days), preventing the use of conventional cross-correlation methods. Assuming a solar-like differential rotation law with two independent parameters (equatorial rotation rate Omega_eq and rotational shear between pole and equator dOmega), we reconstruct Doppler images for different values of the two parameters, and derive the optimal Omega_eq, dOmega and associated error bars from the corresponding chi^2 map. Simulations show that Omega_eq and dOmega can be recovered with good accuracy, even if the phase coverage per rotation cycle is poor, provided the total data set is long enough. From observations of the HR 1099 K1 subgiant secured in 1998, 1999 and 2000, we obtain that the equator rotates faster than the pole with a rotational shear about 3 times smaller than solar.