Two novel conjugated copolymers utilizing 4,7-dithien-2-yl-2,1,3-benzothiadiazole (DTBT) coupled with cyano (-CN) substituted vinylene, as the electron deficient moeity, have been synthesized and evaluated in bulk heterojunction solar cell. The electron deficient moeity was coupled with carbazole and fluorene unit by Knoevenagel condition to provide poly(bis-2,7-((Z)-1-cyano-2-(5-(7-(2-thienyl)-2,1,3-benzothiadiazol-4-yl)-2-thienyl)ethenyl)-alt-9-(1-octylnonyl)-9H-carbazol-2-yl-2-butenenitrile) (PCVCNDTBT) and poly(bis-2,7-((Z)-1-cyano-2-(5-(7-(2-thienyl)-2,1,3-benzothiadiazol-4-yl)-2-thienyl)ethenyl)-alt-9,9-dihexyl-9H-fluoren-2-yl) (PFVCNDTBT). The optical band gaps of PCVCNDTBT (1.74 eV) and PFVCNDTBT (1.80 eV) are lower than those of PCDTBT (1.88 eV) and PFVDTBT (2.13 eV), which is advantageous to provide better coverage of the solar spectrum in the longer wavelength region. The high $V_{oc}$ value of the PSC of PCVCNDTBT (~0.91 V) is attributed to its lower HOMO energy level ( 5.6 eV) as compared to PCDTBT ( 5.5 eV). Bulk heterojunction solar cells based on the blends of the polymers with [6,6]phenyl-$C_{61}$-butyric acid methyl ester ($PC_{61}BM$) gave power conversion efficiencies of 0.76% for PCVCNDTBT under AM 1.5, 100 mW/$cm^2$.