To obtain a work permit for South Africa you must already have a contract of employment with an employer in the country. The employer has to provide a copy of the contract together with documentary evidence that it was impossible to fill the vacancy from within South Africa. (This includes a copy of the advertisement which advertised the job in the South African national press, together with details of all the applicants for the post and a statement of the reason why none of the applications was accepted).
If, as you say, there aren't a large number of vacancies for your type of work, then it's extremely unlikely that you'll get a work permit.
Sorry!
Source:
http://www.home-affairs.gov.za/documents/IMMIGRATION%20R EGULATIONS%20FINAL_excl%20Annexure%20A.pdf
Chris