The 31-year-old socialite and the 21-year-old Spanish model have taken part in a number of "fun" activities during their jaunt on the island of Maui including ziplining on Monday, and the blonde beauty has fallen in love with the island and its "beautiful" scenery.
In a series of posts on twitter, she wrote: "Another beautiful day in Paradise. I love Maui!
"Having a fun & adventurous day in Maui! I love ziplining, the scenery is is beyond beautiful here!
"So much fun zip lining with @RiverViiperi today. I love having adventures in Maui! (sic)"
River also took to twitter to reveal he is having the "most amazing time" with Paris, but it hasn't all been fun for the Calvin Klein model as he broke his phone after it got soaked in the sea.
He tweeted: "Please note that if you are trying to contact me my phone and i went for a little swim today, and he clearly doesn't know how to swim (sic)"
The couple flew to the sun-drenched island last Saturday shortly after a recording of Paris telling a friend in the back of a taxi that she thought a lot of gay men "probably have AIDS", and branded them "disgusting" for being promiscuous, was released online last week.
She apologised for insulting gay people in the recording - which took place on September 7 - saying she is sorry "from the bottom" of her heart for her comments.