If you want it to match the sounds you're looking for, go with jeymS. It doesn't fit standard Klingon phonology, but it's the closest you'll get to "Jay-mes".
If you want to go with canon, then Emeads suggestion of jemS is what you have. This is more the way it's said in TOS.
I believe the "ay" sounds you are looking for is actually "ey" in Klingon transliterated using (can't remember the word for it right now) the non-pIqaD script. It looks like this: in pIqaD.
Note… I'm not a fluent Klingon speaker or any kind of expert, but I think "jemS" is the way James T. Kirk is spoken and written according to the canon (and knowing James T. Kirk is important to the language — look it up if you don't recognize it ;). So, if you want to go with that as a precedent, I would use that.. even though it is pronounced something like: "jehmsh" The whole name (jemS) looks like this: (sorry about the spacing/formatting… I had trouble getting it uploaded. The last letter should be more in line with the first three)