what rubber to buy for wooden wheels
You could cut up an old bike tire. Cut off the sides, and you have a nice strip of actual tire tread. There are lots of different sizes of bike wheel, so you can customize the depth of the tread by choosing between road tire (skinny tire, shallow tread), off-road (much wider tire and deeper, bumpier tread), hybrids (a cross between road and off-road) and those fat balloon tires that have become popular recently.
You could secure the tire tread with thin nails, strategically hidden between the treads. If the nails are too visible once they're in, add a dab of black paint to the nail head.
Or, if you just want a thin layer of rubber, cut up an old inner tube. In this case, there's nowhere to hide the nails, so I would make them part of the design. Space them evenly around the circumference. I would go with a larger nail with a wider head (eg, carpet tacks). Stretch the inner tube slightly as you secure it so it doesn't stretch after the fact and sag or gap. But don't stretch it so much that it will pull against the nails and rip. Note that the nailheads will stick out just a bit, like hobnailed boots. So this is not a good idea if you expect your children to play with these strollers on your nice wood floors.
Thanks to Chris H for this suggestion:

You could glue inner tube rubber - not with patch cement but with contact adhesive or gel superglue. Neither will hold against attempts to peel the rubber away, but should work in this case. This wouldn't work for a tyre, as that's too stiff.

Ask your local bike shop if they will sell you an old tire or inner tubes they were going to throw away. It should be cheap; they may even give it to you for free (especially if you tell them it's for a hand-made toy for your children).