The main focus of the existing approximate arithmetic circuits has been on ASIC-based designs. However, due to the architectural differences between ASICs and FPGAs, comparable performance gains cannot be achieved for FPGA-based systems by using the approximations defined, particularly for ASIC-based systems. This paper exploits the structure of the 6-input lookup tables and associated carry chains of modern FPGAs to define a methodology for designing approximate multipliers optimized for FPGA-based systems. Using our presented methodology, we present SMApproxLib, an open source library of approximate multipliers with different bit-widths, output accuracies and performance gains. Being the first open source library of FPGA-based approximate multipliers, SMAp-proxLib can serve as a benchmark for designing and comparing future FPGA-based approximate arithmetic circuits.