I run the online signups for our athletic booster club as each athlete's family is required to do 10 hours of service per season. We use
Volunteer Spot to manage who, what, when and where. You can send a private link to selected email addresses, get email notifications of who has signed up and where you still have open spots, and it's free. You can define jobs by type (trailer towing) or by day (who is bringing breakfast and lunch during build season for a particular day).
My faith community is using it for managing volunteers for gardening, funeral lunches, etc.
Works well on mobile browsers, accessible from anywhere, scales nicely to small and large needs and has report export features. Set up is easy. The only thing I don't like is that I can't "lock out" edits within a certain time frame, but I do get emails when people back out of an assignment. I can text message or email the volunteers if something changes at the last minute
PM me if you want more detail.
Julia