We report the detection of luminous CO(2-1), CO(3-2), and CO(4-3) emission in the strongly lensed high-redshift quasars B1938+666 (z=2.059), HE0230-2130 (z=2.166), HE1104-1805 (z=2.322), and B1359+154 (z=3.240), using the Combined Array for Research in Millimeter-wave Astronomy (CARMA). B1938+666 was identified in a `blind' CO redshift search, demonstrating the feasibility of such investigations with millimeter interferometers. These galaxies are lensing-amplified by factors of mu_L~11-170, and thus allow us to probe molecular gas in intrinsically fainter galaxies than currently possible without the aid of gravitational lensing. We report lensing-corrected intrinsic CO line luminosities of L'(CO) = 0.65-21 x 10^9 K km/s pc^2, translating to H2 masses of M(H2) = 0.52-17 x 10^9 (alpha_CO/0.8) M_sun. To investigate whether or not the AGN in luminous quasars substantially contribute to L_FIR, we study the L'(CO)-L_FIR relation for quasars relative to galaxies without a luminous AGN as a function of redshift. We find no substantial differences between submillimeter galaxies and high-z quasars, but marginal evidence for an excess in L_FIR in nearby low-L_FIR AGN galaxies. This may suggest that an AGN contribution to L_FIR is significant in systems with relatively low gas and dust content, but only minor in the most far-infrared-luminous galaxies (in which L_FIR is dominated by star formation).