I'm not an expert on paring knives, so take everything I say with a grain of salt.
Make them from thin stock. Some people will tell you that 3/32" at the spine is the thickest you should go, some people say 1/16" at the spine is the thickest you should go. In my personal experience, 3/32" looks awful thick on a paring knife. This pretty much rules out 1084, unless you've got a special source of it or you're willing to spend a lot of time on a surface grinder.
The blade should be short: 2-3.5". Some people say 3" is the longest you ever want a paring knife to be, but that's a personal preference. You should be able to choke up on it and use the tip for fine trimming, and much past 3" does get a little bit weird for this. Handle should be long enough to get a good grip on it, but not so long that it gets in the way when you're choking up. The paring knives in my kitchen have just over 4" handles. Don't focus on handle:blade ratio, just make a handle that is the right size to get the right grip on and a blade that is the right length to do what it needs to do. Narrow, thin handles are traditional, but some people are making them with big handles these days because they're supposedly more comfortable for people with arthritis. I've never tried this so I can't comment on it.
The blade should be narrow so it can cut in a tight radius. The edge should be very thin, but keep it thicker behind the tip — some paring cuts may involve twisting and you don't want a fine tip to break off in your food.
I've heard people say that paring knives should have a lower hardness than most other kitchen knives, because of the aforementioned twisting that may happen to them. I can't comment on this from personal experience.
- Chris