Many janitorial stores carry products designed to remove red stains from carpets/upholstery .
The process is to apply the product directly to the stain, let sit for one minute, brush lightly to agitate, then blot with a clean white towel , then place a heating iron over the towel. It may need two or three applications to remove the stain , and depending on how long the stain has been there you may not be able to fully remove it.
One last piece of advice. If possible take the piece of furniture outside , or have plenty of ventilation, as the product I use is ammonia based and has a very strong odor.
This is a tried and true stain removal answer for red liquid stains (such as red colored drinks) IF they are caught while they are still wet or very newly dried. Windex glass cleaner. When I discovered how well it worked I called the company and asked why they didn't advertise this. They told me that they knew how well it worked but it will sometimes take the color out of an item so they couldn't endorse the use on fabrics. So be careful.