I have a new recliner that slides on the carpet everytime you sit.

try rubber casters

Rubber or felt coasters. They also make chair mats.

Have you tried to put strips of rubber under the rocker, maybe this would keep it in one area. Best wishes. J.

Thanks, it does have rubber there now.

Use a strip of non slip mat

Gjudi, I don't know what kind of recliner you have you state that it doesn't have feet so I have to assume it's either flat to the ground or a rocker recliner. The other suggestion that I have since you didn't take to the plastic or rubber mats which I can understand because they're unsightly, is to make your own mat. You can actually purchase the fabric that matches a recliner from whomever you bought it from unless, it was from a department store such as Walmart or Target but even then the manufacturer sometimes will supply if you give them a call, with the fabrik at a cost. You can also just purchase fabric from any fabric store or hobby store or even a department store and make your very own matte with a color choice similar or that matches your decorating scheme or theme. If you are not comfortable sewing a mat then there's the option of using a hot glue gun to form a mat. And I can help you with either of those options. Let me know if you need any help. By the way if it is a rocker recliner, you could put rubber tape on the bottom of the rockers and it should keep it from skidding.