You'd have to explain it:
* キャプテンモルガンとコーラ (Kyaputen Morugan to Kōra): This is the most literal translation, using the brand name "Captain Morgan" (キャプテンモルガン - Kyaputen Morugan) and "and Coke" (とコーラ - to Kōra). This is perfectly understandable, especially if you point to the bottles.
* キャプテンとコーラ (Kyaputen to Kōra): A slightly shorter version, omitting the brand name. It might work in a setting where it's clear you mean Captain Morgan.
* ラムとコーラ (Ramu to Kōra): This translates to "rum and Coke," which is the generic version. This is the safest option if you're unsure if they know Captain Morgan.
Therefore, ラムとコーラ (Ramu to Kōra) is probably the best option for general understanding. Otherwise, use キャプテンモルガンとコーラ (Kyaputen Morugan to Kōra) and be prepared to point and confirm.