Since my stories are set in the eighteenth century, either in the fledgling United States or (like my current work in progress) the Colonies, it's easy for my characters to be European transplants from one country or another, complete with their national flavor of the English language.
For decades I've been a fan of The Brother Cadfael mysteries, a series of medieval mysteries written by the late Ellis Peters, featuring the intrepid and often loose-footed Welsh monk, Cadfael. But other than turning to those for a guide for rendering a Welsh accent in my character's dialogue (keeping as far away as I can from creatively phonetic misspellings that often hamper a reader in making sense of dialogue), I was at a loss for how to give a distinctively Welsh cadence to their speech. So I went Googling. And found this highly entertaining website:
How To Do A Welsh Accent
If you like what you see (and hear) here, then look to the right for many more short tutorials on various accents by voice coach Gareth Jameson. I'm not sure how helpful these videos will be in my attempt to render accented dialogue on the page, but I found them addictive, and thought I'd pass them along to anyone else who happens to be as fascinated by other people's accents as I am.
A few more examples:
How To Do A Scottish Accent
How To Do A French Accent
How To Do A Cockney Accent
How To Do A German Accent
Edited to Add: Looking for another example in published fiction in which the point of view character is Welsh? Look no farther than Faded Coat of Blue, by Owen Parry. It's set during the American Civil War, so it has a historical feel to it as well. Even though it's an American setting, Abel Jones is Welsh through and through. Even the narrative has a rhythm to it that, to my ear at least, sounds Welsh.
Update: I've also picked up a copy of How Green Was My Valley, by Richard Llewellyn. I haven't finished this book so I can't recommend it as of yet, just offering it up as another possible source for writing a Welsh accent.