The current trend is to use the country's own name sign for itself. In other words, to use the Japanese sign for JAPAN and so forth. A good resource for many of these "updated" country names is ASL Browser.
This seems to be pretty well accepted among younger signers but at least in my area, there is a feeling among older ASL users that there is no need or use for such political correctness, since ASL is about visuals and the "slanty eyes" sign is merely a visual description, not a racial slur. It's a pretty good example of American hearing and American Deaf culture clash. I guess I'm too HEARING-MIND because it does bother me to use the older signs.
