Supporting Graduate Medical Education at Community Hospitals Act of 2019 This bill revises payment rules under Medicare for graduate medical education (GME) costs with respect to a hospital that establishes a new medical residency training program. If a hospital has not entered into a GME affiliation agreement, the Centers for Medicare & Medicaid Services (CMS) must establish the hospital's full-time equivalent (FTE) resident amount only after determining that the hospital's medical residency training program trains more than 1.0 FTE resident in a cost reporting period. If a hospital has an approved FTE resident amount that is based on other specified thresholds, the CMS must give the hospital the opportunity to have the amount reestablished when the hospital begins training FTE residents in excess of the applicable threshold. The bill also establishes similar thresholds for new determinations of certain adjustments to hospital payment limitations regarding FTE residents in allopathic and osteopathic medicine; a hospital that has an adjustment has the opportunity to have it redetermined once the applicable threshold is exceeded.