I would Highly suggest this pairing if you enjoy a medium cigar. I add a squirt of lime to the Private Stock, personally. The stick has a woody after taste that echos perfectly the hint of oak that is present in the rum.
I have tried pairing it with the rum mixed with Coke, but find the drink becomes very close to Vanilla Coke and a bit too sweet to me to pair with the smoke. If you prefer a mixed drink I would suggest mixing it Ginger Ale.