Are they both completely broke? I would put them on the "free" area on Craigslist. But be sure to say they are broken. People may want to fix them up. At least you will get them out of your house. Or call up churches or homeless shelters. See if they want them.
Call the town hall and tell them you want to speak to someone in sanatation. Tell them you have furniture to ge rid of and want to know if they will dispose of it for you. I had to dispose of a couch and recliner also. Thy came by my home and the sanitation men got rid of it.
In El Paso we put things on the curb and they are gone over night. Scavengers from Juarez roam the city looking for cast offs. They never take things from anywhere except curb side! Those poor folks need all the help they can get now that there is little or no tourist trade.