I was digging through the wood storage looking for something to do.   I found a "kit" of a hall table that I got at an auction many years ago.   The maple top is rounded on the front edge and straight on the back, sort of "D" shaped.   Also is a skirt  that is similarly shaped, but only runs across the front.  I opened the stretch-wrapped package of legs (cherry) to what I expected to be 4 legs and there are only 3. So the questions are:
 

1) Should I make another leg or do something like this, one on each end and one in the center?  (there is no bottom shelf in the kit)

 

2) The leg stock is roughly 2x2 and I was thinking of just making a half-lap onto the skirt and tapering the legs.  How much is a good taper for legs like this that are about 29" long?  I don't want to do too much and make it very delicate looking nor so little taper that it's had to tell that it's  even tapered.

Here's another option, but this seems that it would be tippy

The taper in the second photo looks about right to me. I'm guessing (since I couldn't use dividers on the computer screen that the bottom of the legs are about 1/2 the width/depth of the tops of the legs. That might make a good starting point. As for arrangement, the first photo has more eye appeal to me...and i suspect you may be right about the second one being tippy.

I had one of these once.  Would tip over if you farted hard.  Finally had enough and got rid of it. LOL

I would go with "option one" for the best look and balance.  You could do the legs and use a piece of plywood for a test top.  Wouldn't need to be cut round just mount the legs as you would if it was round. 

It is called a demi lun or half moon table and since is designed to against the wall the first picture is right I think as Dan said

I see a lot of these hanging around in the shops and homes of the flintlock crowd....assuming it's early American ?

Here is a taper that I did on a small corner table a few years ago.

 

From what I have seen that style table is backed up to the wall which gives it more stability. I don’t think using it free standing would work well. I agree it would be very prone to tipping. Might even consider attaching it to the wall. 
Paul

I have seen a few half moon tables with 4 legs vice 3 legs.  On the 4 legged version, you have one at each end of the backside, the other 2 would be about where the legs are on tippy table (#2).