(update) It was a typo
Donald Trump has an unfortunate history of typos and misspellings in his tweets:
From the original source cited by the OP, posted 31 May 2017, come the following The Washington Post quotes
Trump targets ‘negative press covfefe’ in garbled midnight tweet that becomes worldwide joke
At 12:06 a.m. Eastern time Wednesday, President Trump tweeted a strange sentence fragment.
“Despite the constant negative press covfefe,” the tweet read. That was it. It ended abruptly, as if someone stopped him, or he stopped himself, or perhaps he never meant to send it.
No, “covfefe” isn’t a typo, at least, not on the part of The Washington Post.
The word “covfefe” does not appear in the Merriam-Webster dictionary. When searching for it on the company’s website, the dictionary suggests “coffee,” “coven,” “cover,” “covet,” “covey” and “cuvee.”
Clearly, it isn’t an English word. Some tweets employing “covfefe” offer the option to translate it from Norwegian, though that appears to be a glitch of some sort. “Covfefe” does not appear to be a Norwegian word, either.
The Washington Post reporter, Travis M. Andrews, clearly stated that “covfefe” was garbled, a typo-tweet committed by the President of the US, a “nonsense” word unlisted in M-W, and not English. Is there any reason for a reputable newspaper journalist, and a native American English speaker, to lie about something so trivial?
Covfefe has attracted its own misspellings on the Internet:
Covfefe (whatever) blazed in the night sky for two brief nights. It's possible that some or many American speakers will want to perpetuate this term, but I doubt it will survive the summer.
Does anyone still talk about the POTUS's infamous misspellings/typos: Barrack (Barack), tapp (tap), and unpresidented (unprecedented)?
Update, 21st July 2017
Donald Trump's “neologism” is still uttered in talk shows and used in social media. Even though I do not visit Facebook, nor have I an Instagram or a Twitter account, I am a keen covfefe watcher and today I spotted an exciting new development in the etymology of covfefe. Martin Gholami has figured out the true meaning of the term.
And elsewhere on YouTube:
covering up federal felony
mid 2017: blend of covering up, federal, and felony.