We present results from a systematic infrared (IR) census of R Coronae Borealis (RCB) stars in the Milky Way, using data from the Palomar Gattini IR (PGIR) survey. RCB stars are dusty, erratic variable stars presumably formed from the merger of a He-core and a CO-core white dwarf (WD). PGIR is a 30cm J-band telescope with a 25deg^2^ camera that surveys 18000deg^2^ of the northern sky (DE>-28{deg}) at a cadence of 2 days. Using PGIR J-band lightcurves for ~60 million stars together with mid-IR colors from WISE, we selected a sample of 530 candidate RCB stars. We obtained near-IR spectra for these candidates and identified 53 RCB stars in our sample. Accounting for our selection criteria, we find that there are a total of RCB stars in the Milky Way. Assuming typical RCB lifetimes, this corresponds to an RCB formation rate of 0.8-5x10^3^yr^-1^, consistent with observational and theoretical estimates of the He-CO WD merger rate. We searched for quasi-periodic pulsations in the PGIR lightcurves of RCB stars and present pulsation periods for 16 RCB stars. We also examined high-cadenced TESS lightcurves for RCB and the chemically similar, but dustless hydrogen-deficient carbon (dLHdC) stars. We find that dLHdC stars show variations on timescales shorter than RCB stars, suggesting that they may have lower masses than RCB stars. Finally, we identified 3 new spectroscopically confirmed and 12 candidate Galactic DY Per type stars - believed to be colder cousins of RCB star - doubling the sample of Galactic DY Per type stars.