Kindergarden Place in Köpenick

There are 69 kindergartens in Berlin-Köpenick. You can find a list on
    https://www.berlin.de/adressen/kinderga … /koepenick
This might not include private child care facilities in your home language, for which it is probably best to ask your embassy.
Since Berlin, like most big German cities, has a shortage of childcare spaces, it might be difficult to find one and there might be waiting lists. It is best to visit each facility you shortlist, not only to get your own impression, but also because their personal impression of you might matter in the selection process.
Since (at least theoretically) any child above 1 year is entitled to a kindergarten space by law, you can also approach your local Jugendamt to get this guaranteed place (but it might not be in your desired location or offer the care hours you want).
Alternatively, you could look for a private nanny.

^^
Great answer. Not much more to add, other than the fact that it helps to be diligent. Finding a space is tough. Get on as many wait lists as you can and follow up regularly.