I have found when teaching learning and physically challenged students that most could learn rhythms and songs by practicing with a partner for each child, as needed. Here are some of my techniques -

Partner and child sit on the floor, or sit together on a bed, or partner sits in a chair facing child who is sitting in a chair. While working on the floor, child sits cross-legged in front of partner, facing forward so that his back faces partner. If needed, partner holds child's right wrist with right hand and left wrist with left hand, so that partner can lead child's clapping pattern.

Students watch as the teacher claps the starting pattern:
1, 2, 3, 4 / 1, 2, 3, 4 / 1, 2, 3, 4 / 1, 2, 3, 4 / etc.

Students pick up the pattern by watching the teacher, feeling the rhythm within themselves. Now everyone closes their eyes, and by listening follows the clapping pattern in unison when the teacher changes it. One set of hand claps is followed by one set of floor claps; repeat sequence over and over.

Note to teachers: While the students eyes are closed, silent claps can be included by clapping with hands and then resting hands in lap for 1 or 2 claps. Repeat the sequence till the dancers are repeating it:
1, 2, lap, 4 / 1, 2, lap, 4 / 1, 2, lap, 4 / 1, 2, lap, 4 / etc.

Clapping the rhythms of different time signatures;
one possible version is given for each, as well of examples of songs:

4/4 time
1, 2, 3, 4 / 1, 2, 3, 4 / 1, 2, 3, 4 / 1, 2, 3, 4 / etc.
"Red River Valley"; "My Grandfather's Clock"; "Alouette"; Evening Prayer from "Hansel and Gretel" by E. Humperdinck; "Hark! The Herald Angels Sing" by E. Mendelssohn.

2/2 time
Clap the pattern of the previous exercise of 4/4 time, except clap twice as fast:
1, 2, 3, 4, 5, 6, 7, 8 / 1, 2, 3, 4, 5, 6, 7, 8 / 1, 2, 3, 4, 5, 6, 7, 8 / 1, 2, 3, 4, 5, 6, 7, 8 / etc.
"Sailor's Hornpipe"; "Jingle Bells"; "There Is a Tavern in the Town."

2/4 time
All hand claps; no floor claps. Accent the claps with numbers.
1 & 2 & / 1 & 2 & / 1 & 2 & / 1 & 2 & / etc.
"Oh, Where Have You Been Billy Boy, Billy Boy"; Brother, Come and Dance With Me from "Hansel and Gretel" by E. Humperdinck; "Mary Had a Little Lamb"; "Baa, Baa, Black Sheep"; "Bobby Shaftoe.

3/4 time
1, 2, 3 / 1, 2, 3 / 1, 2, 3 / 1, 2, 3 / etc.
"The Man on the Flying Trapeze"; "Hey Diddle Diddle"; "Rock-a-bye Baby"; "Pat-a-Cake, Pat-a-Cake, Baker's Man."

6/8 time
1, 2, 3, 4, 5, 6 / 1, 2, 3, 4, 5, 6 / 1, 2, 3, 4, 5, 6 / 1, 2, 3, 4, 5, 6 / etc.
"The Farmer in the Dell"; "Hickory, Dickory, Dock"; "Humpty, Dumpty"; "Here We Go Round the Mulberry Bush"; "Jack and Jill."

For more on teaching adaptive rhythms and movement click on this link - Teaching Adaptive Rhythmic Movement Tips

Article by Susan Kramer

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For offline reading

Adaptive Dance and Rhythms for all Ages with Basic Lesson Plan, has practical adaptive techniques to teach basic dance movements, floor exercises, clapping rhythms, and expressive dance. For kids and adults, illustrated, 47 pages.
Adaptive Dance and Rhythms for all Ages

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About the author
Susan Kramer has been teaching students of all ages and abilities as a Dance Specialist since 1965.