thank you for sharing your question with the Wefugees Community!
I looked into your question and what I could find is that your parents could probably apply for a so called "visitor" or "short term" visa (up to 90 days). They would have to apply for it a the German Embassy in Sri Lanka. They can either apply for a national visa (only for Germany) or for a Schengen-visa which allows them to travel through the Schengen-States (most of Europe).
Via this page of the German Embassy in Sri Lanka you find all the information necessary you need as well as the application form: https://colombo.diplo.de/lk-en/service/01-visaeinreise?openAccordionId=item-1589116-4-panel
Please keep in mind that for private visits, an invitation is usually required to confirm the purpose of the journey. In case the visitor is not able to fully cover the costs of their trip and stay in Germany a declaration of commitment has to be presented with the visa application ("Verpflichtungserklärung") - which is basically a declaration of another person living in Germany to take care of the costs. The person who sends the invite can sign it at the local authorities (Ordnungsamt or Ausländerbehörde). But there are some requirements like a legal residency in Germany and proof of enough money to cover the costs.
Here you can find more information about the specific requirements: https://www.germany-visa.org/verpflichtungserklarungen/
Also be aware of the fact that the Embassy can reject the visa application - applicants are not entitled to receive a visa.
I hope, I could help you with this information. Please get back at us if you have more questions!
I wish you all the best!
Note: Please keep in mind that we can´t provide qualified legal advice via the internet and that any information given can´t replace such legal advice.