Okay, hopefully I understood the assignment right.
I have 24 rounds where 12 teams are paired up with
each other.  The best configuration I can come up
with is below.  Each letter represents a team.  Each
line represents a round.  In your case I think that
means that the first three lines are for the first
monthly meeting, etc.  Really, you can use the lines
in any order you want, I put no significance on that.
The worst characteristic of this chart is that team B
and team G only play each other once.  Everybody else
plays each other two or three times.  I was unable to
fix the team B and G quirk.  There is a table below
that gives all the details.

As is usual for my assistance, since I've spent many
hours on the program and a couple of hours running it
and tweaking it for your request, I insist that you
put my copyright message on any copy of this or any
chart that you derive from this arrangement.

Have fun and I'd appreciate hearing any feedback.
--
Paul Chamberlain, tif@tifster.com


Best Configuration for 12 teams playing 24 rounds:

	AB CD EF GH IJ KL
	AC GJ KL DF HI BE
	AD FL EH BC GK IJ
	AI EJ DK GH CF BL
	AJ FG HL BK EI CD
	BF HK DG AI CL EJ
	BH DI CE JL GK AF
	BJ AH EG CF DL IK
	CG BI FJ EL HK AD
	CK EL GI DJ AF BH
	DE CK HL AG BJ FI
	DG BC FH IL AE JK
	DL AF BK EI CH GJ
	EG CI AJ FK BL DH
	EH JK BD AL FG CI
	EK CH IL BF DJ AG
	FI JL AK CG EH BD
	FK GI CJ DE BL AH
	FL BE AC HJ DI GK
	GL DH BI AK CJ EF
	HI EK FJ CD AB GL
	HJ AL BD IK FG CE
	IL BG AC EJ DK FH
	JK DF GI BH AE CL
	Copyright 2006, Paul Chamberlain (tif@tifster.com)

Who plays who:

	  A B C D E F G H I J K L
	A . 2 3 2 2 3 2 2 2 2 2 2
	B 2 . 2 3 2 2 1 3 2 2 2 3
	C 3 2 . 3 2 2 2 2 2 2 2 2
	D 2 3 3 . 2 2 2 2 2 2 2 2
	E 2 2 2 2 . 2 2 3 2 3 2 2
	F 3 2 2 2 2 . 3 2 2 2 2 2
	G 2 1 2 2 2 3 . 2 3 2 3 2
	H 2 3 2 2 3 2 2 . 2 2 2 2
	I 2 2 2 2 2 2 3 2 . 2 2 3
	J 2 2 2 2 3 2 2 2 2 . 3 2
	K 2 2 2 2 2 2 3 2 2 3 . 2
	L 2 3 2 2 2 2 2 2 3 2 2 .

Who sits where:

	Table 1: 5 4 3 4 4 4 4 4 4 4 4 4
	Table 2: 3 4 5 4 4 4 4 4 4 4 4 4
	Table 3: 4 4 4 4 4 4 4 4 4 4 4 4
	Table 4: 4 4 4 4 4 4 4 4 4 4 4 4
	Table 5: 4 4 4 4 4 4 4 4 4 4 4 4
	Table 6: 4 4 4 4 4 4 4 4 4 4 4 4