You have two options: Prettier - the Ladder Stitch, and Stronger - the Baseball Stitch.
First, the Ladder Stitch.
Quoting the linked site:
First, poke your threaded and knotted needle through the bad side of one cloth, ensuring that the knot is on the inside of the plushie. Next, pass the needle partway through the good side of the other piece of cloth at the closest location where the pieces meet. Don't pull the thread too tightly; you'll need space to perform the next step. Now that the tip of your needle is on the inside of the plushie, pass it through to the outside and pull the whole needle out. Repeat. Remember to pull the earlier stitches tight at some point, once you don't need the wiggle room.
This one, when pulled taut, closes neatly, holding the two halves pretty much flush with each other and looking very neat, but it isn't quite as strong as the latter, and when mistreated, it will just pull apart, revealing the needlework, crumpling the cloth laterally, and losing the whole appeal.
The Baseball Stitch - same as on a baseball ball, except pulled taut such that it forces the material to fold and crumple, is much stronger, but when pulled taut, the sides don't form such a neat, flush connection, but form a shallow groove, and the needlework may be visible if one peers into it.
Just push the needle from the inner side of the material onto the outer, and cross to the other side, repeating, inner to outer. When pulled taut, it crumples the material left inside into two "bars", which provide tension to the stitch preventing it from coming apart, and pressing against each other pull it inside, forming the characteristic groove. It requires much more force to break and doesn't crumple the visible surface of the cloth when strained, but if it does come apart somewhat, due to abuse, the needlework will show more, and even perfectly new it will form a deeper and more visible groove than the Ladder stitch.
Let me add that in your situation, where you're repairing items that were already subjected to abuse and likely will continue to, the baseball stitch is a better choice, as despite worse initial appearance, it doesn't degrade nearly as much when abused.
