I know I've fixed it in Swaddlebees fitteds before (and others), but it was a while ago and I can't remember now if it was an OS or sized, or if it matters... anyway, here's what I did, no sewing machine required!
You should be able to feel the ends of the elastic, a slightly thicker part at the top and bottom of the thigh section. Once you think you have the right spot (or near enough), you should be able to gently pull apart the seam where the inner and outer fabrics meet (easier to spot on a nappy that has a coloured outer and natural inner, but you should be able to find it if yours is all natural too). Unpick the seam so you have about a 1" opening, and find the end of the elastic. Do the same at the other end.
Cut a new piece of elastic (I think about 5" long, I remember measuring against a Bic pen - the length of the pen up to the bottom of the cap), and stick a safety pin through one end. Cut the old elastic at both ends, leaving a short stub (3-4mm), and pull it out, then stitch the non-safety-pinned end of your new elastic securely to the old elastic's stub. Then feed the safety pin through the hole and pull it out the other hole. Stitch the other end of your elastic to the other stub, then close up the holes as tidily as you can.
You can replace back elastic the same way. If that's not terribly clear just say, it's kind of hard to explain! It's actually pretty easy, and not really noticeable.