The Bündnis für Familie Tübingen, working with the city of Tübingen, has compiled the leaflet "Kurzzeit- und Notfallbetreuung für Kinder".
It gives a list of various Tübingen providers you could approach in such emergency/ short-term need cases.
This care takes place with a daycare family and is for children between 3 months and 5 years in special cases (conferences, out-of-town appointments).
Note: If your child is sick, you can take a certain number of paid days off to care for him/her, if the child is under the age of 12. More information on this rule here: "When your child gets sick" - organising your work when your child is ill.