We have investigated the magnetic and magnetotransport properties of wedge-shaped Fe1-xCox/Cr/Fe1-xCox trilayers grown by molecular-beam epitaxy on Al2O3 (<1(1)over bar 02>) substrates with the Co concentration x ranging from 0 to 0.2. A completely antiferromagnetic (AFM) coupling with zero remanence is obtained in both pure Fe/Cr and alloy Fe1-xCox/Cr samples at a Cr thickness of about 10 Angstrom. The giant magnetoresistance (GMR) of the AFM coupled Fe/Cr trilayer is about 5.5% at low temperatures. With increasing Co concentration, the GMR effect, Delta rho/rho(s), decreases drastically, having an amplitude of only 0.7% at x = 0.2. In the pure Fe/Cr trilayer, there is a strong reduction of the GMR effect with increasing temperature. In contrast, the GMR of the samples with alloy magnetic layers is only weakly temperature dependent because of an increase of the net change of the magnetoresistance, Delta rho, with temperature. The strong decrease of the GMR effect in the alloy trilayers is tentatively ascribed to the possible loss of the band matching of the minority-spin band, which is important in the Fe/Cr superlattice. The temperature dependence of Delta rho at finite temperatures can well be interpreted by introducing a positive linear temperature term together with a negative quadratic term, which are attributed to spin-dependent electron-phonon scattering and spin-flip electron-magnon scattering, respectively.