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Rihanna Need An 'Umbrella' For That Tequila ... Taking Shots in Barbados!!!

Rihanna's getting rowdy down in the Caribbean ... downing shots with some friends at a beach bar in Barbados -- and, lifting a glass to her one-year-old son.

The singer-songwriter hit Thunder Bay Beach Bar on the small island country ... pulling up with a trio of friends to the spot this weekend and ordering tall shots of what looks like tequila, limes at the ready of course.

The four ladies pose for a pic before RiRi tells everyone to put their glasses in the air ... all while a worker at the bar films.

Rihanna asks the worker for her name, and she responds it's Rose -- a name that gets Rihanna's eyes to light up since it's her son Riot's middle name.

The group then has to raise a glass to her infant son -- born just over one year ago -- and, while you don't see Rihanna actually put the glass to her lips, it's pretty clear she's ready to down a drink.

BTW ... Rihanna asks if Rose can drink on the job -- and, when Rose says yes, tells her they need to take a shot together.

Just Rihanna in the clip BTW ... no A$AP Rocky or the kids joining her on this late-night excursion -- even though we know she's in Barbados with them.

Remember, last week photogs captured Rihanna and Rocky going for a quick dip with their boys. Cute family photos ... but, looks like Rihanna needed to let off steam on vacay too.

Bottoms up, Rihanna ... and, someone get her an Umbrella for her drink!

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