The Aaron Copland Fund is an organization worth looking into for music studio grants. It awards grants for various music related causes and music studios. Studio owners can apply for the Recording Program grant, which deals specifically with recording contemporary American music and the distribution of it after recording. (Aaron Copland Fund: coplandfund.org.) The Canada Council for the Arts has grants available for professional non-classical musicians that can be used for funding music studios as well. (Canada Council for the Arts: canadacouncil.ca.) The National Endowment for the Arts has grants available as well that can be used for music studio funding. (National Endowment for the Arts: nea.gov).
The Paul Hamlyn Foundation awards grants for various organizations and issues such as social justice, along with support for the arts. The arts grants listed vary but the money can be used for music studio funding as well, due to the non specific natures of some of the grants available. (Paul Hamlyn Foundation: phf.org) The MacArthur Foundation awards "Genius" grants to outstanding innovative musicians that have been used to fund music studios as well. (MacArthur Foundation: macfund.org)
Looking into state and local sources of funding for starting and running a music studio can be even easier then the application process required for applying for national grants. Local arts commissions and even Kiwanis clubs have available funding.