I'm looking for something like doodle but I want the participants to submit where they are not free. So I can find dates based on this. I think it could be easier to do this way around.
It's been a while, but maybe it'll help someone.
You can do this with https://pollunit.com
In the "Advanced schema settings" you can select "Lowest resistance" as target. This allows your participants to cast negative votes. This works for dates, free text, images etc.
I am one of the developers.