When looking online in dictionaries, I can't figure out what word to use to say the following:
An article I wrote has been published in a newspaper.
Are any/all of these correct?
発刊 is "to publish (an entire issue)". 著す is a (relatively uncommon) literary verb that means "to author/write (a book)." 掲載 is a reasonable word choice, but 掲載する is transitive.
After fixing the transitivity, we get:
(I noticed) (someone) had kindly published an article I wrote.
While this is now grammatical, this is a fairly nuanced sentence. For one, ～てくれる is probably not necessary unless you really have a reason to say it. For one, ～ていた means you just noticed the article had been already out for a while.
A natural way to say "～ is now published" is actually much simpler:
私が書いた記事が新聞で掲載された。 (or 掲載されました)