These are the rules we use for the Eskgammon tournaments. We added anteing up when a player gets eliminated from the tournament to speed it up but otherwise it should be pretty close to GE swing tournaments.

Swing rules:
 Entry fee gives you 12 chips (manual swing tournaments, automated web tool ones can be set per tournament)
 Jacoby
 No Automatics
 Preferred ending (see below) + Speed up ending
 One match at a time (means finished matches are recorded in order, several matches can be in progress at the same time of course)
 When a match ends its result is recorded and a new opponent is immediately assigned (if possible),
    i.e. even if another match ends during assignment the first result is processed entirely first
 Match results must be recorded immediately (not after a toilet break)
 Starting ante = 1
 Ante goes up by 1 every time an opponent drops (or every new match if the finale)
 Ante goes up by 1 every 15 minutes (manual swing tournaments, automated web tool ones can be set per tournament)
                             In a manual tournament a clock is used for ante ups and optional tour breaks are held as needed and the clock is paused
                             In an automated tournament, once an ante up is scheduled, the clock is not reset for a new ante up until someone *completes/posts* a match
                             (i.e. the ante up time is not as "fixed" - in a normally progressing tour it will effectively be the roundtime as matches complete fast -
                              however, if a tour "pauses" the clock also holds as there is little point advancing the clock if everyone is taking a break)
Ante does not change for a match in progress
All-in active (i.e. if you have less chips than required to offer/take a cube you go in with as much as you have and can also only win as much)
Players leaving the tournament (i.e going home) will continue to lose starting chips of each match they will play until they are eliminated (theorethically a player could thus even return). This also handles major breaks (like half an hour, agree beforehand that you will forfeit until you return). Not being available for an entire round (15 minutes) would be considered extremely bad behaviour (and at that point other players may vote you a "leaving player", i.e. your forfeits begin).

Player assignment:
Starting assignment according to dice rolls or whatever suitable method and after that matches get resolved one by one and the rules below apply.
Of the unassigned players the chip leader and the chip loser are assigned against each other first (repeat for the remaining players if possible, then record the next match result (in order, ONE at a time)). The chip leader is determined once another match has ended, i.e. the chip leader when players are waiting is *irrelevant*.
Two players that played against each other in the previous round cannot play again (until the finale), this means on occasion the chip loser has to sit out.
If the chip leaders tie the chip leader is the player who was chip leader the previous round.
If the chip losers tie the chip loser is the player who was chip loser the previous round.
If chip leader/loser ties cannot be resolved looking one round back, whoever is first in the list is selected in manual tournaments and randomly in automated tournaments.

Note: "round" means looking back at previous chips one round earlier. Some players might have played lots of matches more than other players so there is no actual round in a swing tournament except for stake/time purposes.

Originally optional rules (but recommended and nowadays already default rules):

Preferred ending: Once only two players remain the tournament ends according to current status once the finale chip loser loses his first match. This speeds up the finale immensly and gives the chip leader a (slight) advantage which is fair anyway. In practice this means the chip trailer always doubles (and the leader has an option to take) and the finale is concluded as soon as the initial chip loser gains enough chips to "survive" one match and still remain chip leader.

Speed up ending: Once only two players remain a maximum of three matches are played after which the tournament is adjudicated according to current status.

Play time:
We have tested with 10/15/20 chips earlier but for some reason 12 seems quite good for most player amounts. Around 6-12 players in a tournament can be expected to have one tour running 2-3h using a 15 minute ante up.

Manual bookkeeping:
It's definitely preferable to use the Swing tournament tool for tournament bookkeeping. However, if you don't have a laptop or tablet (or even smartphone) available recording the tournament manually and entering it into the Swing tournament tool later (for statistics purposes) is perfectly ok. Look at the picture below to see how a tournament in progress would look like. Here are some tips on how to do it as it's not simple to enter a tournament later if the games aren't recorded in order.

Setting up players and chosing chip amount etc is trivial.
Each assigned match should be given some identification (A+A, B+B). Since match completition order is crucial it is almost impossible to reconstruct a tournament without this information (or having a huge amount of luck). The letters of the alphabet are usually enough for 4-8 player tournaments.
Record current stakes as 1, 2, 3 etc below the main sheet. I would recommend having a timer on repeat and adding the times when the timer fires OR a player is eliminated. While recording the times isn't necessary it will give you a better picture of how fast a swing tournament really progresses, regardless of the amount of players.

Misc:
Swing manual bookkeeping example

 Change log:
 2016.10.08 Player leaving tournament added. Endings used added to default format.
 2016.12.22 All instances of the word "game" changed to "match" (just a few). Swing tournaments work best as money games. However, with less chips 3p or 5p matches could also be played. However, as tournaments would drag on forever even with 4 chips I would suggest an additional MATCH cube is added when playing. i.e., in addition to having the 3p match cubed as normally another cube would be added that determines the stake of the match. It would be distinct from the cube used in the match and switch from one player to the other just as a cube normally does. While it might be faster to have the match cube also double stakes it might create unforseen problems. In any case, the thought of playing #p matches is added mainly for IBA purposes and has never been tested in practice.
 2017.01.03 Added a picture of how a manual tournament would look (bookkeeping).