Dirty diapers belong in the garbage.
However, there are programs that collect diapers separately for recycling. Usually these companies service daycares and the like, and sometimes local residents can participate. You could look into that. It would be more effort than curbside pickup, though. Additionally, if you remove the plastic backing, in most cases the rest of the diaper can be composted in your own compost bin (but it not suitable for municipal collection).
Remove the backing all you want. The diaper still contains human waste. It is bio-hazard no matter how you look at it. That being said, they need to go to either a landfill, or a facility that can incinerate them. Question my position on the environment all you want, but, my soiled diapers go straight to the landfill...
When it comes to selective waste collection, where do they belong to? Assuming plastic backed diapers.