there are a couple of Kindergärten in Solingen. See the list on the following link:
All these institutions want you to call them (just click on the links and scroll down to find the phone number). Then you get an appointment where you can get to know the Kindergarten and the people there. Hopefully they have some free places left.
Keep in mind that there is a huge demand for Kindergärten which is why it can be quite time consuming to find a place.