During 25 years of teaching post and rung chair making I have recommended the 5/8" Stanley Powerbore Bit with a brace and bit extender for the horizontal boring of rung tenon mortises. The Stanley bit, with one nicker and one lip was easy to drive. The slender spear point was easy to shorten. See the Video, Make a Chair from a Tree, available through  www.greenwoodworking.com   Some years ago Stanley discontinued its line of Powerbore bits and I have received numerous and sometimes exasperated inquiries about a replacement. Subsequently I learned that Lee Valley manufactures and sells a bit essentially identical to the Stanley Powerbore.
         However, in the interim, I discovered superior tool.. It is made in Austria by Stern and sold by Diefenbacher Tools 1-800-326-5316. Item No. 570-3510. It has two nickers and two lips. Both the nickers and the unthreaded lead point are small and require no modification. The bit is far more accurately made than the Powerbore and will hold up well. The metal is harder.The bits configuration makes it twice as aggressive as the Powerbore.

    The 5/8" Universal Bit shank diameter is .308". I could not find a commercially available bit extender with a 5/16" (.3125") inside diameter socket. Brian Boggs suggested making an extender from 5/16" diameter water hardened drill rod and a matching setscrew coupling. MSC Industrial Supply, 1-800-645-7270, Item No.06010201 and Item No. 35465731 The rod and coupling cost about 1/2 that of an extender (if you could locate one). The rod is shipped in 36" lengths. You can make the extender any length you desire and, if necessary, the brace end of the rod can be filed to a tapered shape. I use my extender in a brace with a Universal chuck. The two-setscrew coupling works well though it is only 1" long. File a slight flat on the both the bit shank and the drill rod.   
 
john alexander/greenwoodworking
1/25/02
 
One woodworker replied:
 
 Thanks for the information on a replacement bit for the power bore. This is the nicest bit I've have seen in a long time. Had to run some experiments when I got it. (This is just the way I am.) Used in on things like plywood, air dried pine,air dried maple, and kiln dried red oak. In all of this material it cut an absolutely smooth hole. Used it under power and in a brace.  When I used the brace, I did not find it all that hard to bore a mortise. It did seem to have a problem clearing out chips. For the time being, I'm going to use it the way it is, and not do any modifications. But if I decide to modify it, it does not appear to be too difficult. On the subject of extensions, all of the extensions I can find have a 1/4-inch bore. There are two solutions for this problem. The first way is to have a machine shop bore out the extension to 5/16 inch. ( I have access to a machine shop, so this procedure does not cost me anything.) The second method is to take the bit to a tool grinding shop and have the shank ground down to 1/4. If one does not have access to these facilities, then Brian's method is the best route.
 
JA: Extender accuracy is better when drill rod and coupler are used. Available extenders are often sadly bent or the head is not centered on the shaft.