How can I repair my leather couch?

There’s always duct tape. (Is that the sofa arm? If so, try antimacassars)

Brown duct tape

Try something like this 3M leather repair.

I found this instruction for Magic Mender which is probably the same stuff @Tropical Willie has linked.

You can buy a thin leather patch about the same color and apply it with contact cement [or there is something similar call shoe goop I think]—contact cement is the adhesive contractors use in building projects and shoemakers use to get leather resoles to adhere to the old shoe. I say “thin” leather so it won’t show as much and because if it was an inexpensive leather couch, that leather is probably thin, too, maybe even backed with fabric. You might make the patch into a shape so it looks like a bit of applique design and use a tint or shade of original leather color.

@anartist is correct, get a patch. I have had my leather couch for eight plus years and I keep a thin quilt on it for my dog to prevent nail scratches and holes. If you can’t keep them off when you’re gone, try unfolding newspapers and laying them on top of it, dogs don’t like the sound or feel of newspaper.