Here is what i would do if I was in your position. I would see how hard it is to take the seat and upholstery apart {that being the kushion and the pad}. If it was not too difficult, I would then get a small piece of vinyl as close to the existing color as possible, and perhaps back the tears with it, sort of making a patch but on the inside. I would use Shoe Goo to glue in place the patches, and make sure the outside hole was as neat and tightly closed and flush as possible. I would then reassemble the seat; and would use Shoe Goo again to re-glue the material back down to the pan. This is not very quick or easy to do, but it might would work and look good and provide a decent repair; you should see what other people say on this thread before attempting any of this. They might have a better idea. Alternatively, you might could glue and or stitch the vinyl patches to the outside which would be easier, but a lower quality and likely less durable fix and probably would not be very visually appealing.
It also depends on how supple and strong the vinyl of the seat still is. Vinyl has a tendency to sometimes grow brittle and prone to rip with age.