These resources are likely to have cimbalom and cimbalom parts available for sale.

https://cimbalombohak.sk/en
This is the website for the company that makes cimbaloms inspired by famed instrument maker Lajos Bohak and true to his approach. The original factory was located in Budapest, Hungary, but now is housed in Slovakia.

//cimbalom.hu/en/
This website is a great resource for information about purchasing, new and used cimbaloms and cimbalom parts. Cimbalom mallets, or sticks, for example, are available here. You can find photos of the instrument’s construction, too. This site refers to the instruments as cimbalos.

//www.cimbalomkeszito.hu/
Akos Nagy has a workshop in Budapest where he makes smaller-format cimbaloms with 3.5 octaves (vs. 4.5 octaves on concert-size instruments). Akos can build to spec, too. He doesn’t speak English but does a lot of business with foreigners, and he can translate English emails.
His email address is acymbal.66@gmail.com

Cimbalom mallets, or sticks, can also often be found at https://www.etsy.com