Hi,
I was wondering the same thing myself. I called one place to volunteer, and I left a voicemail since no one picked up, and I did not receive a response. I called another place, and they told me that they are currently accepting student volunteers so she gave me the email of the volunteer coordinator to contact. I sent her an email, and I never received a response. I also work full time from 8-5pm, most places close shortly after 5pm, and most PT places around here are not open on weekends. I recently started the job too so it is difficult for me to get some time off so I understand how it is.
I have talked to a few people though, and they said that if you can, try to take a little bit of time off to go and talk to a pt volunteer coordinator in person instead of trying to contact by email. It will look better to that person, and you will more than likely be able to find volunteer work that way. Also, be persistent. Don't just contact them once and not contact them again if you do not hear a response. They want to see that you really are truly interested in volunteering. Good luck!