From your description, you are engaged in a "not for profit" activity. As such, you deductions are limited to your income and can only be reported on Schedule A (itemized deductions). If you don't normally itemize, you effectively don't get any deduction and the entire $300/month is income.
Even on Schedule A, you may not deduct your payment. You may deduct "regular" car deductions ("cost recovery method that is applicable to your type of vehicle") like interest, insurance, and depreciation.
See IRS publication 525, particularly pages 17 & 32. https://www.irs.gov/pub/irs-pdf/p525.pdf
