Availability date advertiser and scheduler (calendar)

I’m currently building a site for a deaf-blind association. The site is aimed towards the deaf-blind and the people volunteering to help them (contacts). My client has asked if I could somehow create a page with a calendar where the deaf-blind and contacts could make arrangements. For instance; if a contact is available one day, he would be able to make himself available for the deaf-blind in the calendar on that date and vice versa; if a deaf-blind needs a contact one day, he can advertise it in the calendar.

Since several deaf-blinds and contacts could be advertising on the same date, deaf-blinds/contacts should be able to mark the ad or delete it.

Is there any plugin or any way I could do this?

Thank you!