Guy Clark has been of Austin City Limits five times that I know of. I am still tring to fill in the information about each. They were:
October 30, 2001
March 28, 1998
December 15, 1977

In March of 2000, ASCAP honored Austin City Limits for their 25th anniversary. Guy was the special guest host, pictured here are (l) ASCAP's Herky Williams and (r) ACL's producer Terry Lickona.
(Photo by Audrey Haynes)

October 30, 2001. Lyle Lovett: Step Inside This House
Lyle and his band played "Step Inside This House," followed by Guy playing:
Red River
Cold Dog Soup, with Lyle singing harmony

The photos below come from Steven Fromholz's site. I borrowed them in case he changes his pages around. Steven says in regard to the show, "One of the great things about events like festivals and tapings is the time I get to spend with friends and colleagues I may not get to visit with often. Guy Clark is still as gangly as ever, and his performance on that show was mesmerizing."

These photos come from Vince Bell's photo gallery.

March 28, 1998. A Celebration of Townes Van Zandt.
The show was actually taped on December 7, 1997. An impressive lineup: Jack Clement, Lyle Lovett, Rodney Crowell, Emmylous Harris, Willie Nelson, Guy Clark, John T. Van Zandt, Nanci Griffith, Peter Rowan, and Mickey Raphael on harmonica.
To Live Is To Fly Guy Clark
This is followed by an emotional introduction: "So we just gonna take turns up here, tell lies . . . stories and sing songs that Townes Van Zandt wrote."
No Lonesome Tune Peter Rowan, w/Nanci Griffith, Mickey Raphael
Forth Worth Blues Steve Earle
Tecumseh ValleyNanci, James Hooker
The Highway Kind John T. Van Zandt
Guy says "cheerful little ditty . . . definite dark side . . ."
Pancho and Lefty Willie and Emmylou with Townes' original perfomance edited in
If I Needed You Emmylou and Steve Earle with Townes' original perfomance edited in
Heavenly Houseboat Blues Rodney Crowell, Emmylou, and Jack Clement
Lungs Lyle and Steve
For The Sake Of The Songs Jack Clement,
Guy says, "I knew Townes for 35 years I guess. This is one of the first songs I think I ever heard him sing, and it may be the first song he ever wrote, or at least one of them. This is absolutely seameless. If you're a writer this is what you want to be copying."
Don't You Take It Too Bad Guy with Townes' original perfomance edited in
White Freight Liner Blues Everyone

Evidently, this was not the same order of the perfomance. An email to the Townes list had the following set lies:

Intro - Guy Clark
To Live To Fly -- Guy Clark
No Lonesome Tune -- Peter Rowan w/ Nancy Griffith
Brand New Companion -- Steve Earle
Tecumseh Valley -- Nancy Griffith (w/ her bandleader)
Ira Hayes -- J.T. Van Zandt
Pancho & Lefty -- Willie Nelson and Emmylou Harris
If I Needed You -- Emmylou Harris and Steve Earle
Heavenly Houseboat -- Rodney Crowell w/ Emmylou Harris
Flyin' Shoes -- Lyle Lovett
For The Sake Of The Song -- Jack "Cowboy" Clement
Don't You Take It Too Bad -- Guy Clark
I'll Be There -- Peter Rowan
Fort Worth Blues -- Steve Earle
The Highway Kind -- J.T. Van Zandt
Pueblo Waltz -- Rodney Crowell
Lungs -- Lyle Lovett and Steve Earle
White Freightliner -- Whole Group (led by Steve Earle)

November 10, 1989.
This show is from the Old Friends era, and has Stuart Duncan on fiddle and mandolin and Edgar Meyer on bass. I haven't fully verified this as an ACL show, but the set list was:
Texas, 1947
Old Friends
Come From The Heart
Desperadoes Waiting For A Train
Doctor Good Doctor
Better Days
Homegrown Tomatoes

November 11, 1981.
Willie Nelson followed by Guy Clark.
L.A. Freeway
Who Do You Think You Are?
Partner Nobody Chose
Rita Ballou
The Last Gunfighter
The South Coast Of Texas
Texas Cookin'

December 15, 1977, Recorded August 31, 1976 . Guy Clark followed by Steven Fromholz.
He is joined by Danny Rowland on guitar, Charlie Bundy on bass, and Chris Laird on drums. It is very interesting to note that at this time, ACL's theme song was Texas Cookin'. I'm not sure why they would change that! (Not to take away from Gary P. Nunn's "London Homesick Blues," though.)

Last Gunfighter Ballad
It's About Time
Captain Flint and Laverne
Virginia's Real
Texas, 1947
Desperadoes Waiting For A Train
Texas Cookin'

Here's KRLU's
main listing for Guy. I have added to it, so I put this link at the end.