Being a volunteer who has a disability and uses a service dog falls into a unique area when requesting a reasonable accommodation to be accompanied by your service dog at the volunteer site. The Equal Employment Opportunity Commission (EEOC) covers employees with disabilities who use a service dog.
A volunteer does not meet the criteria of employee, and has no legal protection under federal law to be accompanied by their service dog while volunteering. This also may apply to volunteers serving AmeriCorps or Vista. The stipend that the volunteer receives is not considered a wage or salary, additionally the person is a volunteer and not an employee.
This is not to say that a service dog user and the volunteer site coordinator or supervisor cannot negotiate an independent written or verbal contract allowing their volunteer to use their service dog while volunteering.
Some states have taken a creative and proactive position on their volunteers who have disabilities and use service dogs to mitigate their disabilities while volunteering. To locate information on this, one might look under their state office of volunteerism and tourism, or ask their state office of civil rights if volunteers with disabilities who use service dogs may use their service dog at their volunteer site.