Renovate and Enhance Veterans Meeting Halls and Posts Act of 2019 or the REVAMP Act of 2019 This bill requires the Department of Veterans Affairs to carry out a pilot program to award grants to veterans service organizations in rural areas to (1) repair or rehabilitate a facility in a rural area, and (2) acquire or upgrade computers and technology for such a facility. An organization may not receive a grant in any fiscal year in an amount exceeding the lesser of (1) the aggregate cost of such proposed activities and uses, or (2) $75,000. An organization that receives such a grant for a fiscal year shall be ineligible for any such grant for the next five fiscal years. Grants awarded under this bill may not be used for the construction or acquisition of new facilities.