毎日、ニュース記事をひとつ読んで頑張っている I'm making an effort to [read a news article every day]

sounds fine to me, as long as you move the を to after 記事 (ひとつ should be used adverbially).

To me, this formulation doesn't sound like the material is difficult to you. More like keeping up the habit is difficult. If, on the other hand, you say

毎日、ニュース記事をひとつ頑張って読んでいる I'm [making an effort to read a news article] every day

it's more likely to sound like the material is difficult to you.

毎日、ニュース記事をひとつ読んで頑張っている I'm making an effort to [read a news article every day]

sounds fine to me, as long as you move the を to after 記事 (ひとつ should be used adverbially).

To me, this formulation doesn't sound like the material is difficult to you. More like keeping up the habit is difficult. 

If, on the other hand, you say

毎日、ニュース記事をひとつ頑張って読んでいる I'm [making an effort to read a news article] every day

it's more likely to sound like the material is difficult to you.