I know that distributing spirits can be tough--there are lots of old, established networks out there and lots of new entries clamoring for shelf space. Bottom line, the end consumer dictates who carries what, so tastings are critical. You can do this at private events/fundraisers as well as at local and regional gourmet food events (and, of course, at your bar).
In terms of brand awareness to the wholesale buyers, put an ad in a trade paper, do direct mail and/or do a branded e-mail campaign to the buyers you want to sell to. Host a launch party at your bar and film it, then post the film (which of course should have LOTS of testimonials on how great the rum is) on YouTube.
Send out an e-mail blast to everyone you know to watch the video and spread the news to their friends, peers and business associates. Get people to blog about it and discuss it on various social networking platforms (MySpace, Facebook, etc.).
To create additional end-user awareness among clients and prospects (which in turn should boost requests for their local retailer to sell this new brand), create a Caribbean-themed event at your bar with T-shirts and prizes. Send a press release to your local papers at least four weeks before the event and one with pictures after the event. Tie your event to helping a local charity (like a food bank), which helps to promote your product and do some good things for your community at the same time
There are lots of other creative things you can do to promote and sell your rum. Check out my website for other penny-wise marketing tips.
Wishing you success,