Can ている be used for stating activities that are not being performed habitually

So I hope I understand your question here, and this answer makes sense.

First off your eg. sentence works. It implies that you do read the paper, but not everyday.

Lets say you want to use a different time delimiter than everyday; we could use たまに. We have two options for this, Positive and Negative, and both effectively mean the same thing while using opposite logic.

私はたまに新聞を読んでいる

私はたまにしか新聞を読んでいない　　(Note the use of しか～　vない）

You could also say something like, 毎日読んでいないけど、週4回読んでいます。

Hope that Helps.