Is the 2nd image (one below the google translate) more accurate? Is the のですが just completely wrong or?
Also I know the Google translate is wrong at the end because I accidentally had a new line after "call".
Both machine translations are not very natural. I would translate this as:
I want to call him but I'm sleep so I won't call him tonight.
- 彼に電話したいのですが、眠いので今夜はしません。
- 彼に電話をしたいのですが、眠いので今晩はやめておきます。
Either way, の before ですが is perfectly natural. This type of の is called explanatory-の, and it's perfectly natural to use it to set up a context, as in your sentence. See the "preliminary remarks" section in the linked article. See also: What is the meaning of ~んです/~のだ/etc?
Besides, you need a contrastive-は after 今夜/今晩. This is something easily forgotten by English speakers, but it's important.