Hello Ellen,
Jokes in music are quite current, they are part of the composers’ sense of humor, of their culture. The composer integrated them to his pieces with the purpose of them being musical jokes so they are not dependent on the relationship piece-performer for existence, but you got obviously performers who can perform the joke part better than others. In the funny composers I would put in general the French: Satie, Saint-Saëns, Debussy and Ravel. Partly because a musical joke can often be expressed in a sound effect which is what French music is very interested in. Saint-Saëns has some very funny parts in his Carnaval des Animaux (I’m thinking of the Contrabass-Elephant or the two pianists attempting a C major scale). The Russian neo-classics are full of black humor and ironic jokes. Especially Prokofiev, there is something funny about the intervals and harmony in his music.
The Romantic composers weren’t very strong in their sense of humor, I can’t think of one humoristic effect by Chopin (I would be happy if any of you found some and share here), Brahms and Liszt are serious too. The romantic composer who stands out for me in his sense of humor is Schumann with his play of words-notes and his different characters (well, Florestan is a very witty character). Again, Carnaval is a subject where composers can express their sense of humor and playfulness, Schumann has written two, his op. 9 (over 4 letters A.S.C.H) and the Viennese Carnaval op. 26.  The lettres dansantes, and coquette from op.9 are funny pieces where he uses for example the little appogiaturas to create this light and playful effect.
In the classical period the most humorous composer is in my opinion Haydn. He went into great lengths in discovering all the possible ways to make a musical joke, from putting in loud instrumentation right at the parts where he knew his old ladies’ audience was falling asleep, to protest about the musician’s conditions in that symphony where they all leave, to other musical effects connected with harmony, rhythm and structure. There is one last composer I wish to add as having a good sense of humor, it is Bach. It is never the jokes that one laughs out loud at, it’s a quiet one, but one can’t avoid recognizing his wit by the way he uses the same motives in different rhythmical options, creating thus many word games.

Sometimes in classical music "jokes" are almost only private ones, for initiated people. For example, there is an unexpected big one in the scherzo (third movement) of Bruckner's Sixth Symphony. Unexpected, because Bruckner has a reputation as a very serious and rigorous composer. But in this movement, more precisely in the "Trio" -that means the central part of it- Bruckner almost ridicules one his most serious themes, that means the principal one of his Fifth Symphony (and this symphony is today known for being ascetic -an adjective I don't agree with...). But listening to this movement of the Sixth Symphony without knowing this Fifth Symphony, who can ear this explicit ridicule...? So, it's a private joke, as is Mahler's Scherzo of his Second Symphony.
 

As to Chopin's sense of humour, the examples are  not  very numerous...but  I maybe found  one : The waltz op64n°1 in D  flat major that is sometimes nicknamed "little dog waltz".  I dont't know if  the anecdote is true or  if it is  a legend (maybe someone here  will  be able  to tell me?) but  it  is said that Chopin thought about  George Sand's dog  running  round  in circles  and chasing its tail when he composed this waltz. The fast tempo and the melody that seems to spiral in  on  itself   create a funny  effect corresponding with  the  movement of  the  playful  dog.
As to Haydn, spontaneously I think  about  the  final  movement  of the sonata HobXVI 34 in E  minor. For  me, this  movement  is emblematic of Haydn's music and  sense  of  humour. Through Haydn's imagination, mastery  of contrasts (by  contrast, passages  with a  kind of  melancholy when juxtaposed  with  playful ones,  emphasize these) variations and  modulations, one  is often caught  by surprise and  has  got the  impression  that anything may happen at any time.And I interpret Haydn's indication  "innocentemente" on the score as childish, spontaneous, mischievous, playful and somewhat humourous attitude.
In the  classical  period, In addition  to Haydn,   I would mention Mozart himself and for example two of his very famous pieces :  the "Turkish  March", a  pastiche, a caricature  of the turkish  style through its characteristic rhythm and the  variations  on "Ah  vous dirais-je Maman"

As to Bach, his  playful spirit appears in  his works through his mastery of structure.
As  a French person, I  would  like  to make an allusion to his famous Badinerie from the Orchestral  Suite n°2. The badinerie is  a brief and lively dance in  the  baroque period and it derives from the french word "badinerie", synonym of "plaisanterie"...that  means .joke!