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The Merian survey is mapping 850 degrees2 of the Hyper Suprime-Cam Strategic Survey Program (HSC-SSP) wide layer with two medium-band filters on the 4-meter Victor M. Blanco telescope at Cerro Tololo Inter-American Observatory, with the goal of carrying the first high signal-to-noise (S/N) measurements of weak gravitational lensing around dwarf galaxies. This paper presents the design of the Merian filter set: N708 and N540. The central wavelengths and filter widths of N708 and N540 were designed to detect the Ha and [OIII] emission lines of galaxies in the mass range 8 to 9 by comparing Merian fluxes with HSC broad-band fluxes. Our filter design takes into account the weak lensing S/N and photometric redshift performance. Our simulations predict that Merian will yield a sample of 85,000 star-forming dwarf galaxies with a photometric redshift accuracy of $Delta z/(1+z)= 0.01 and an outlier fraction of eta=2.8% over the redshift range 0.058<0.10. With 60 full nights on the Blanco/Dark Energy Camera (DECam), the Merian survey is predicted to measure the average weak lensing profile around dwarf galaxies with lensing S/N 32 within r<0.5 Mpc and lensing S/N 90 within r<1.0 Mpc. This unprecedented sample of star-forming dwarf galaxies will allow for studies of the interplay between dark matter and stellar feedback and their roles in the evolution of dwarf galaxies.