Published prestige class for "Monk with a sword"?

[ken-ichi]

If you do go for the feat to allow flurry method, a possible Prestige Class could be Dervish.
This would allow your monk to utilize his speed and mobility while also allowing him to utilize his multiple attacks from flurrying. With a full BAB progression with bonuses when using the dance, it might give the monk the needed bonuses to get some hits in. This PrC has moderate prerequisites so a level or two in another class may help obtain them.
A fighter/monk in my Eberron game is going that route. He will actually be taking the first Dervish level next time.

 

[Samothdm]

Not a PrC or a feat, but a few issues back in Dragon, in the "Class Acts" section, there was a slightly altered monk class that allowed the use of a few martial weapons with the Flurry of Blows ability. There were a couple of trade-offs for allowing that (can't recall what they were off the top of my head).

 

[Wish]

The Player's Guide to Arcanis has a nice set of monk pclasses and monk orders (variations on the monk base class), including one with longsword ability.

It's a pretty good book in general, with lots of interesting monk and paladin variants, and a ton of feats. It would take some work to port parts of it to a non-Arcanis campaign, but the monk orders and classes would be easy enough. They're religion specific, but you can strip the references to religion easily, and you're left with some cool monk orders.

 

[Elder-Basilisk]

I'll second the Player's guide to Arcanis recommendation.

If you pick it up, the sections you want to look at:

Monk class:
Order of the Blade monk and Blade of Hurrian prestige class

Feats:
Martial weapon technique

 

[Shellman]

Another option,

The City of Shelzar source book from the Scarred Lands Campaign Setting has a Shalzari Knife Fighter class with some very nice abilities that stack with Monk abilities if you have monk levels.