The Content Photobomb
If you really want to annoy and irritate your website visitors make sure that you block the content they were enjoying by pop-up newsletter sign ups and other marketing ploys. Make it hard to find the X to click them off.
But be careful, since January 2017, Google has begun to penalize mobile websites that hide content behind popups (read more on the Google Webmaster website) but it is still totally okay to do this on Laptops and PC's.
You can make sure you are annoying your visitors by tracking your visitors' reactions on Google Analytics, a high bounce rate and low return visitors means that you have been successful at irritating your victims, ahem, visitors.
As an example of Cute versus Annoying, one of the sweetest things in TV commercials have been llamas that appear behind the action of the advertisement. To be annoying do the opposite:
Selfie with Llama--Cute
Llamas at Wedding--Cute
Man with Llama--Cute