Ah yes, that was one of the pictures that came up in my searching too, but it's an Elvish ship I do believe. Not that Elvish ships wouldn't be useful for inspiring a Numenorean ship, actually, because the Elves taught the Numenoreans a whole lot.
By the looks of it, we're pretty much on our own as far as pictorial representation goes, then. I'm ashamed I haven't got any textual descriptions, but I left my library back home across the Atlantic!

Let's see what we can piece together:
1. The Elves made ships inspired by swans.
2. The Elves of Tol Eresseä taught the Numenoreans many things, hence Numenor's incredible "advancement" over the other Mannish races of Middle-Earth.
3. I think some Numenoreans sailed to the Grey Havens on Middle-Earth (either ferried by Elves, or in their own rudimentary ships) to learn shipbuilding from Cirdan.
4. The rough technological period of Real-Life history that all Three Ages of the Sun mirror is the Norman Conquests, roughly 1000 years ago. (Not, I might add, the 500 years Peter Jackson raves about in the Two Towers DVD.) This is probably why all the pictures we've been able to find look roughly like Longships.
5. The Numenoreans were to the Men of Middle-Earth as the Romans were to the "barbarians." (Roughly speaking.)
6. The Numenoreans took ship building to a neurotic level, such that they ran out of trees on their island and had to rape the Western shores of Middle-Earth for timber...thence their early colonisation activities.
7. From #6 I think we can surmise that they built bigger and bigger ships.
8. The Numenoreans sailed every sea there was to sail on in the whole of Arda. They essentially circumnavigated the globe many times over.
So, maybe the following principles can guide your modelling:
1. The elegance of a swan (although not an actual Swan Ship, otherwise there wouldn't be a need to distinguish Numenorean from Elvish ships)
2. The technological level of at least a Knorr...
3. ...but up to something like a civ-Caravel, given the Rome-to-Gaul ratio (?), and the circumnavigation fact.
4. Let it be big, let it be multi-decked and multi-masted, heck give it some oars like tjedge1 suggested (or not?), let it be the next step in Medieval Sailing minus the influence of gunpowder:
By the end of the fourteenth century, then, the three basic generic forms of northern boatbuilding, the knarr or buss, the cog, and the hulk had begun to merge together. There must have been many variations reflecting the practices and regional traditions of the medieval shipwrights, but the tendency was towards convergence on one particular form for large merchant ships. All retained certain basic features. They were all still edge joined clinker built shells. They had stern hung rudders worked by a tiller, or a whipstaff on the larger ships, and they were mostly rigged with a single mast and loose footed square sail. In its composite forms the knarr, cog and hulk were coming to the end of their development. They could not be increased any further in size without the risk of losing their structural resistance to hogging and other wave induced stresses. Nor could their sailing power be increased without adding more masts which in turn required larger and stronger ships. Economic conditions in the fifteenth century demanded new large ships in response to new needs. Firstly they need to be able to undertake oceanic sailing carrying large numbers of men and equipment and sustaining themselves at sea for considerable periods of time. Secondly they needed to be able to mount and deploy guns both for defensive and offensive warfare. The introduction of artillery to naval warfare precipitated a radical change in the design of the medieval ship.
Your ideas for modifiying the Cog might fit right in. Obviously, I have no clue what I'm talking about! Sorry for not being more of a help.
From there, I guess, let your imagination run wild...and see what everybody thinks? (On utah's LotR unit preview thread?)