I would like to write my son's name, James, phonetically in Klingon script. From my reading there isn't an "ay" sound in the Klingon language as the a makes an "ah" sound. Should I drop the "a" altogether and just write it as "jms"?
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.