UX pattern for two people to agree a date/time

Background: Freegle allows people to give away things they don't need to other people nearby. Part of this involves agreeing a date/time for collection. People do this by messaging back and forth, but there's a lot of "can you do Thursday evening", "no, but I could do Friday morning", "That doesn't work for me, how about Wednesday afternoon between 2 and 3". People get bogged down in this, and because the system doesn't know what they eventually agreed, we can't send them reminders to help them be more reliable in turning up.

I'm trying to work out a way to improve this process. What I want is a web widget that is a bit like doodle.com, but just for two people to agree a date/time, probably some time in the next week, that works for both of them.

I don't want to ask both people to enter all the times they are available over the next week - that's too much effort and would feel too intrusive. So I need a way to reach agreement with the smallest number of iterations. For example, it could start off trying to establish whether people would prefer weekdays or weekends, daytime or evening, then move on to specific days and times. And it needs to feel helpful, not irritating.

Has anyone ever seen something like this done well?