Here are several pertinent references. Anything in parentheses is my addition to attempt to clarify any vague writing in the originals. I will try to email you this info as well, just in case moderators think this post is too open. Hope this is some help.
Magic Digest, by George B. Anderson, 1972, page 187
"...sew four rings to the four corners of a square of dark, durable cloth. Put the live rabbit on the cloth and draw up the four corners at the top. Put the four rings over..." your headless nail at the back of your table. Anderson's version is using a pair of tubes, and so he hangs his rings on an S-hook that will hang on the top of his tubes.
Modern Magic Manual, by Jean Hugard, ???, page 305
"An easy method is to have the animal in a black bag, the mouth of which has four or five metal rings sewn to it (the implication here is perhaps a circle of cloth rather than a square of cloth, hence the fifth ring to help hold the bag closed). Put the rabbit in, and hang the bag by the rings on a headless nail on the back of a small three-fold screen. In the course of the preceding productions, throw a number of silks over the screen in such a way that in picking them (back) up (a bit later in the production) you can (that is, will be able to) grasp the bag by the rings. When you have the hat empty... pick up the silks and the bag (under cover of the pile of silks) and dump them into the hat, bag first. Discover then that there is something else in it, remove the silks, and bring out the rabbit. The bag must be lined with silks of different colours, part of which are left unsewn (that is, half of each silk is not tack sewn onto the bag's interior) so that when the bag is turned inside out it will pass for a bunch of silks."
101 Easy-to-Learn Classic Magic Tricks, aka 101 Easy-to-Do Magic Tricks, by Bill Tarr, 1977, page 53
"In this case, your load - a rabbit in a bag or whatever - is hanging from a headless nail on the back of a chair onstage. As you bend over to pick up (an object)... or deposit some object on the seat - preferably some thing you have jsut produced from the hat - you steal the load and swing it right into your hat in one smooth, deft, and well-practiced motion." (Page 52 also has two versions from a simple body steal; page 54 has an assistant load, another body load, and a table load.)
Tricks With Hares, by U.F. Grant and Don Tanner, ???, 8 page illustrated pamphlet, page 1
"First of all you require a square handkerchief or cloth about 18 inches square. Sewed in each corner of the cloth is a buttonhole... Lay the cloth out flat on a table and place the rabbit in the center of it. Gather up the four corners and run a cord through them. A ring, about the size of a (personal) keyring, is slid down over the (cord and the) ends of the cloth until it is against the rabbit. This holds the lower section into a bag affair... The cord which was run through the holes in the corners of the bag is tied into a loose loop by a regular bow knot. This loop is hung on a nail at the back of...any draped...table... (After the load, to produce,) slip the loop off the nail... pull the bow knot loose (to) clear the buttonholes and pull the ring up off of the bag." (sic) (There are 8 complete rabbit production versions in this booklet).
I am sure that I can find more in my library if I keep looking, but I think you get the idea.
Jon A. Hand