Although electric vehicles (EVs) eliminate CO2 emissions on the road, the upstream emissions from electricity generation still affect the emissions benefit brought by vehicle electrification. Coordinating EV charging to match the low marginal emission factors (MEFs) of electricity generation could reduce emissions, while aggregating the charging events may create a higher power demand undermining the grid stabilization goal. To address the trade-off between emission reduction and peak power demand shaving, this study developed a bi-objective optimization model for quantifying the relationship between minimizing CO2 emissions and peak power demand. Using one-year EV charging data from a workplace parking lot with 50 charging piles in California, USA, the results show a non-linear relationship between the two objectives throughout the year. Compared to uncoordinated charging, coordinated charging can reduce CO2 emissions by 18% annually while also reducing peak power demand by 33%. However, further reducing emissions by around 1% requires a significant increase in peak power demand by 84%, which is 23% higher than the peak power demand without coordination. These findings provide quantitative insights for policymakers and other stakeholders to balance emissions reduction and grid stabilization goals toward sustainable EV charging coordination.