A couple of things. There is a Charity called HOPE DOLLS that works with abused and neglected children - they come and pick up stuff from your home. Great for all sorts of donations for baby/kids. www.hopedolls.org. If they don't want the car seat, I am sure they would have a good suggestion.
Or, you can just post an ad for it on Craiglist in the baby/kids stuff section. Just say it is free. I am sure you will have someone come pick it up - you can just go to a Starbucks nearby and have them pick it up there if you don't want anyone coming to your home. You can screen the emails or ask them to call you so you can see if you are comfortable having them come by. You can also post when it will be available (date as starting at what time) and just put it on the curb by your home - someone will come pick it up. I have donated a few larger household items this way (e.g., patio furniture, etc), on a first-come-first-served basis.