“Appellate court” sounds like “a pellet court.” “Physicians should always take their legal business to a pellet court” is a pun that was cited in print in May 1888.
 
“When the man was shot with a BB gun, the case ended up in a pellet court” was posted on the newsgroup alt.x.y on January 8, 1999.
 
“In what legal venue would a rabbit seek to settle a dispute over where it is allowed to eat or defecate? A Pellet Court (By Gary Hallock)” was posted on the newsgroup alt.humor.puns on March 14, 1999. The rabbit joke is sometimes included with Easter bunny jokes.
 
   
30 May 1888, Daily Telegraph (Harrisburg, PA), “Little Bits,” pg. 4, col. 2:
Physicians should always take their legal business to a pellet court.
   
Google Books
13 October 1888, The Albany Law Journal (Albany, NY), pg. 304, col. 2:
IT would seem that our Court of Appeals judges are all homeopathics. At any rate, they are a pellet court.
 
Google Groups: alt.x.y
For your entertainment
Jon
1/8/09
(...)
When the man was shot with a BB gun, the case ended up in a pellet court
   
Google Groups: alt.humor.puns
Weekly PUNY Riddles
Stan Kegel
3/14/99
(...)
135. In what legal venue would a rabbit seek to settle a dispute over where it is allowed to eat or defecate?
(...)
135. A Pellet Court (By Gary Hallock)
 
Google Groups: alt.humor.puns
Puns of the Weak: 8/17/01
Stan Kegel
8/18/01
(...)
In what legal venue would a rabbit seek to settle a dispute over where it is allowed to eat or defecate? A Pellet Court   (Gary Hallock)
   
Google Groups: alt.humor.puns
Puns of the Weak: 08-15-03
Stan Kegel
8/15/03
(...)
Where do rabbits settle their legal disputes?
In a pellet court.  (Lederer & Ertner)
 
Twitter
PuterPrsn™‏
@PuterPrsn
When the man was shot with a BB gun the case ended up in a pellet court.
3:47 PM - 12 Apr 2009
 
Twitter
Bollywood Sargam‏
@bollywoodsargam
Rabbit jokes - 8254 Joke: Where do rabbits settle their legal disputes? In a pellet court! .... http://bit.ly/omxBn
12:48 AM - 23 Aug 2009
 
Google Books
A Man Walks Into a Bar 3
By Jonathan Swan
London, UK: Ebury Press
2010
Pg. 21:
When the man was shot with a BB gun the case ended up in a pellet court.
 
Google Books
Sensible Nonsense.. Frank’s Comic Pack:
Humour Pack Series
By Frank Paul
BookBaby
2014
Pg. ?:
Where do rabbits settle their legal disputes?
In a pellet court!