The most authentic opinion is that offering dua in salah during sujood is halal and it is halal to make dua in sujood in your native language as well. Though some scholars have a difference of opinion on regards whether it is permissible for a native Arabic speaker to make dua in Sujood in another language.
Furthermore, it is permissible for a person to offer supplications that were not narrated in hadiths even if that is in colloquial Arabic or in a language other than Arabic, outside of the prayer, or in the prayer when one is unable to speak Arabic, provided that he/she use any permissible words and avoid transgressing the limits, and provided that his supplication does not involve any sin or severing of ties of kinship.
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