The NATO Codename does not have to correspond to its actual name. Counter-example: MiG-29K (9-31) is Codenamed Fulcrum-D.
Seriously, it is MiG-29S (Latin) unless somebody would kindly post a link to a credible, significant source which says otherwise. MiG-29S (1,4 million google hits) vs MiG-29C (0,4 million google hits) so far and plus German, English and Russian wikpedia articles agree on that and they are not direct translations of each other. And also the russian "C" (Kyrillic) is pronounced like an english "S", so it makes sense.
EDIT: http://migavia.ru/index.php/en/production/the-mig-29-fighters-family Even the official MiG page uses the "S" in the "SM" variants etc.