One note: the rules say all entries in this journal have to be friends-locked (even though, yeah, this is just a discussion post, so whatever, no biggie).
Where on earth did you get such a beautiful Vetinari picture?!
I think the trick to writing Vetinari with any kind of a sexual relationship is interpretation. How much do we actually know about him? He seems asexual, doesn't keep a lover as far as we know. What would attract him to somebody, what would turn him on? I think it's more important to find an interpretation of the character, based on canon, that would explain attraction, rather than just pick someone he kind of gets along with. Personally I think he'd be drawn to someone intelligent, though he's also been known to be fascinated by people who are just interesting or unpredictable. But that does seem to be a rather cerebral fascination, sort of like the study of beetles.
I try to avoid writing OCs that have a romantic or sexual relationship with my favourite character. If I do write something like that, I sort of try to make sure it's not the love of that character's life, or anything like it. It's just too easy to find yourself writing a Mary Sue, whatever the gender - also, your OC has to be pretty wonderful - as in a good character, not someone annoyingly perfect - to get the reader to actually care about him.
I hear what you say about Vimes and Vetinari. It would have to co-exist with Vimes/Sybil; and I would never want to break up Vimes and Sybil.
Drumknott/Vetinari seems to work pretty well in the fics I've read. In canon they're very comfortable with each other, apparently Vetinari trusts him perfectly, and Drumknott can even question Vetinari's judgement - it's not a huge leap to assume that level of trust and comfort comes from sharing a deeper feeling. Theirs is a master-servant relationship, though, and that could be a problem in writing them as a couple. Although people seem to get over that too - just look at all the Jeeves & Wooster slash...