Another option is to contact your local recycling center. They may be able to provide you with a recycling bin for Sunday papers and coupons, or they may be able to direct you to a facility that can recycle these materials.
Finally, you can also try contacting the newspaper company directly. They may be able to provide you with recycling instructions, or they may be able to arrange for the recycling of Sunday papers and coupons.
Remember, most stores are recycling all junk mail and newspapers, so they might not have this bin at every location, but it is worth asking about just in case. Some have partnered up with the newspaper company to assist in recycling this paper together already, so there is a good possibility that the employee who you ask will know what you are asking about.