This study focuses on local channel correlation based zero-forcing (ZF) precoding design for boosting weighted ergodic sum-rate (WESR) in the cooperative two-cell multiple-input single-output system. We first present that the WESRs of the statistical channel state information (SCSI) aided general eigenvector coordinated beamforming (SCSI-GE) and the conventional ZF beamforming with erroneous instantaneous channel state information (ICSI; eICSI-ZF) saturate to constant values at high SNR due to inter-cell interference. Motivated by this, we develop a ZF coordination framework with local SCSI requirement at the transmitter and low data-sharing backhaul load. Additionally, a low-cost but effective two-dimensional ZF precoding design called 2d-SZF is proposed, which involves only distributed computations based on the local channel correlation. Theoretical analysis and simulation results confirm that the proposed local SCSI-based 2d-SZF scheme yields the most desirable WESR while the WESRs of SCSI-GE and eICSI-ZF both saturate in the high regime of SNR, and are respectively sensitive to the level of spatial channel correlation and ICSI accuracy at finite SNR.