Nonprofit Relief Act of 2019 This bill amends Internal Revenue Code provisions relating to tax-exempt or organizations to repeal the requirement that the unrelated business taxable income of tax-exempt organizations be computed separately for each trade or business activity, exclude from the gross income of charitable volunteers reimbursement of expenses for the use of a passenger vehicle for the benefit of a charitable organization, and allow the tax credit for employer-paid family and medical leave for nonprofit employers. The bill also increases the corporate income tax rate from 21% to 21.06% (as an offset to the cost of this bill).