Chicago Manual of Style makes a distinction between journals and newspapers or magazines:
In an academic setting, it is generally preferable to use journals in assessments; however, there are use cases for newspapers, magazines and less scholarly journals.
Page numbers may usually be omitted from newspaper references. When citing articles from weekend supplements and other special sections, specific page references may be beneficial.
1st citation
First name Surname, "Title of Newspaper Article: Subtitle," Title of newspaper, Month Date, Year, page number(s).
Jim Yardley and Simon Romero, “Liberation Theology gets Second Look in Pope Francis' focus on Poor,” Sydney Morning Herald, May 30, 2015, 54.
Subsequent citations
Surname, "Shortened Title of Newspaper Article," page number(s).
Yardley and Romero, “Liberation Theology gets Second Look,” 54.
Surname, First name. "Title of Newspaper Article: Subtitle." Title of newspaper, Month Date, Year.
Yardley Jim, and Simon Romero. “Liberation Theology gets Second Look in Pope Francis' focus on Poor.” Sydney Morning Herald, May 30, 2015.
1st citation
First name Surname, "Title of Newspaper Article: Subtitle," Title of newspaper, Month Date, Year, URL.
Zach Hope, “'A new energy': Back to Church for the Tiny Flock Made Whole by Refugees,” The Sydney Morning Herald, June 6, 2020, https://www.smh.com.au/national/victoria/a-new-energy-back-to-church-for-the-tiny-flock-made-whole-by-refugees-20200604-p54zq8.html.
Subsequent citations
Surname, "Shortened Title of Newspaper Article."
Hope, “A New Energy.”
Surname, First name. "Title of Newspaper Article: Subtitle." Title of newspaper, Month Date, Year. URL
Hope, Zach. “'A new energy': Back to Church for the Tiny Flock Made Whole by Refugees.” The Sydney Morning Herald. June 6, 2020. https://www.smh.com.au/national/victoria/a-new-energy-back-to-church-for-the-tiny-flock-made-whole-by-refugees-20200604-p54zq8.html.
1st citation
"Title of Newspaper Article: Subtitle," Title of newspaper, Month Date, Year, URL if applicable.
“David Simmons to Focus on Theology following NRL Retirement,” Daily Telegraph, September 3, 2015, http://www.dailytelegraph.com.au/sport/nrl/david-simmons-to-focus-on-theology-following-nrl-retirement/story-fni3gfvk-1227510512966.
Subsequent citations
"Shortened Title of Newspaper Article."
“David Simmons to Focus on Theology.”
Title of newspaper. "Title of Newspaper Article: Subtitle." Month Date, Year. URL if applicable.
Daily Telegraph. “David Simmons to Focus on Theology following NRL Retirement.” September 3, 2015. http://www.dailytelegraph.com.au/sport/nrl/david-simmons-to-focus-on-theology-following-nrl-retirement/story-fni3gfvk-1227510512966.
1st citation
First name Surname, "Title of Magazine Article: Subtitle," Title of Magazine, Month Year, page number(s).
Tim Beardsley, “Where Science and Religion Meet,” Scientific American, February 1998, 18.
Subsequent citations
Surname, "Shortened Title of Magazine Article," page number(s).
Beardsley, “Where Science and Religion Meet,” 19.
Surname, First name. "Title of Magazine Article: Subtitle." Title of Magazine, Month Year.
Beardsley, Tim. “Where Science and Religion Meet.” Scientific American, February 1998.
1st citation
First name Surname, "Title of Magazine Article: Subtitle," Title of Magazine, Month Year, URL.
Brian Handwerk, “Gospel of Judas Pages Endured Long, Strange Journey,” National Geographic, April 2006, https://www.nationalgeographic.com/science/2006/04/gospel-judas-pages-long-strange-journey/.
Subsequent citations
Surname, "Shortened Title of Magazine Article."
Handwerk, “Gospel of Judas.”
Surname, First name. "Title of Magazine Article: Subtitle." Title of Magazine, Month Year, URL.
Handwerk, Brian. “Gospel of Judas Pages Endured Long, Strange Journey.” National Geographic. April 2006. https://www.nationalgeographic.com/science/2006/04/gospel-judas-pages-long-strange-journey/.