The melody and rhythms used in dancing must be well known for successful dancing. Many dancers do drumming (even if they only learn the rhythms) as well as zills (or finger cymbals). The tambourine can also be used to play the rhythms.
What was used in period was a frame drum, while the drum used today for ME rhythms, the darabouka/ doumbek or goblet shaped drum was shown less often in manuscripts. However, the doumbeks is very well known and can be easy to play. There are metal, ceramic and wooden drums to choose from. Please choose what is best for your circumstance.
There are many instructional books and dvds that teach the rhythms on a doumbek. They are available at Amazon here or you could hire a drummer to come out and teach, like Anne Harkin in Victoria. The best thing to do is ask at a drum shop. And practice!
This is a nice example of a master doumbek player, named Souhail Kaspar. There is another drummer there, playing a frame drum but the song is carried completely by the doumbek player.
This is an article by Rick Dawman, known in the S.C.A. as Baron Edward Shirebrooke about Medieval Middle Eastern percussion.
Arabic Maqam World is an educational website set up to help people learn the modal or maqam system of Middle Eastern rhythms. They also cover musical forms as well as Muwashahat (or Andalusian) rhythms.
Differ to the drum rhythms as they are played by the dancer to highlight the down beat or up beat of a particular rhythm. The zills are on the middle finger and thumb of both hands. What was also used in period was qarkabeb or Moroccan castanets.
Now zilling is usually done in dance class, following the teacher. However, it is also possible that homework is given! Practice until it becomes a muscle memory. If you have neighbours who do not appreciate loud zilling practice, then the zills can be muffled with a small drawstring pouch. I have heard the toe of a sock is excellent to use.
Or you can purchase instructional dvds through Amazon.