If I wanted to do some research for Black History Month, are there any archives (digital or otherwise) for newspapers, magazines, or comics that were made by and catered to the African-American communities in the United States?
The best way to access these archives is through ProQuest (https://about.proquest.com/products-services/news-newspapers/pq-hist-news.html) This is a subscription service, but many libraries provide access to this service. If you scroll down the list, you will see listings for "Black Newspapers". The "Chicago Defender" was probably the most prominent as it played a leading role in providing information to Black Americans during The Great Migration.
Beyond ProQuest, Accessible Archives also has a variety of these papers: http://www.accessible-archives.com/collections/african-american-newspapers/ (this has personal subscriptions available.) I do not know if the large newspapers.com system from Ancestry includes any such papers--the large ones I know, of which the Defender is as /u/ttobaben indicates a key bellwether, aren't represented.
For magazines, these are also often subscription; EBSCO holds the rights to Ebony, for example, and I've not known them to do personal subscriptions that are at all affordable.
For comics, I'm not exactly sure; that's a great question, and I think we do have a comics historian floating around among the flairs, but I can't find them from a cursory search.
These of course all pale in comparison to the large microfilm collections that exist in a number of university libraries and in the USA at the Library of Congress (in hardcopy and film)--but those aren't exactly usable at present. Often by appealing to that fact, you can get temporary access to more expensive institutional resources especially at public universities or state libraries (if in the USA).
Google has some old newspapers digitized and available for free:
The Afro-American Ledger here and here (I don't know why they're separate)
The Voice of the Fugitive, not actually a US newpaper, but a Canadian one founded by someone who escaped to Canada
There may be more there (edit: There definitely are more there but I'm not going add them all to the list). I also found various compilations or individual issues from Black-owned magazines and papers on Google Books eg. here, here and on archive.org here, here, here. This method works best when a) you know what you're looking for and have a title and b) when the papers are old, out of print, and in the public domain. It's not very consistent over time and some issues may be missing, but it's also free and doesn't require any subscription service
I'd recommend browsing through two subscription sites, www.genealogybank.com and www.newspapers.com. You do not have to subscribe to browse their list of papers. If you have a list of papers you want to see, go check out how many they each have. It might be worth a 6 month subscription depending on how.many matches you get. I use both for Civil War era papers and they are great.