Recycling plastic toys can be difficult! It is uncommon to find programs that accept them. The main problem is identifying what type(s) of plastic the toys are made from.
As far as recycling programs specifically for toys, it is a good idea to check with the toy manufacturer to find out if they offer a recycling program for their products. (Like Mattel and Lego®.) If the toy manufacturer does not have a recycling program, you can still let them know that, as a consumer of their products, you expect them to offer a responsible disposal option.
The only other recycling program you're likely to find is run by TerraCycle! TerraCycle runs numerous recycling programs for hard to recycle items. Consumers purchase boxes for recycling a particular category of item, fill up the box and send it back. TerraCycle will then take care of the recycling process. TerraCycle runs a recycling program for toys. Which includes Hasbro, Spin Master, L.O.L. Surprise!™, VTech® and LeapFrog®.
This TerraCycle program is a amazing option, but can be costly. You may want to consider getting together with a few like-minded parents who also have toys to recycle so you can share the cost of the boxes.
As always, The Lorain County Solid Waste Management District is big on "Reuse." If your toys are in Good Condition, please consider donating them back into the community.