In German Standard German it is:
(ending like the pronoun ich)
In Austrian Standard German and in Swiss Standard German there is another form:
(ending in a k-sound, which is the hardened form of g, see Auslautverhärtung)
[ˈlaŋva͡eliç] is allowed everywhere where people speak German, but in the south of German sprachraum (i.e. in Switzerland, Austria and southern parts of Germany) the variation [ˈlaŋva͡elik] is more common.
You can listen to this variation here: http://www.adaba.at/
- Enter "langweilig" in "Orthographische Suche" and klick on the lense.
- In the list above appears all words, that contain "langweilig", will appear, witch in this case is only one word ("langweilig").
- Click on this word in the list
Now you can see the phonetic transcription, and you can listen to 6 professional speaker. From each country (Austria, Germany and Switzerland) you can choose between a male and a female speaker.
I know the voices from the Austrian speakers, they are professional TV-moderators, i.e. educated speakers.
The phenomenon, that you noticed in the word "langweilig" appears in all words, that end with -ig:
Honig macht den König selig.
In Germany you will hear -ich three times. In Austria and Switzerland you would rather hear three times -ik at the end of the words.
Note, that this only happens at the end of a word. In ...
... the pronunciation as "Könichin" would be wrong.