I have read that you can use coffee grounds on gardenias to improve the acidity. Questions-
Can I just pour the (cooled) grounds from my french press around the drip line?
That's false...a myth. Used coffee grounds are fairly close to neutral...the acidity is in your coffee cup.
That being said, coffee grounds are great when added to compost or mulch or as an amendment when preparing a planting bed when used in small amounts. Coffee has some allelopathic properties....used grounds not so much unless used in large quantities.
So, use the grounds to add organic matter to the soil but not to decrease the pH.
If you're talking about an outside shrub in the ground, I think you'd get more mileage out of a few banana peels, buried just under the surface near the trunk. What's making you think you should acidify your soil?