Wikipedia doesn't have much about this language:
The Karen languages are members of the Tibeto-Burman group of the Sino-Tibetan language family. The three main branches are Sgaw, Pwo, and Pa'o; they are not considered to be mutually intelligible (Lewis 1984). Karenni (also known Kayah or Red Karen) and Kayan (also known as Padaung) are related to the Sgaw branch. They are almost unique among the Tibeto-Burman languages in having a Subject Verb Object word order; other than Karen and Bai, Tibeto-Burman languages feature a Subject Object Verb order [8]. This is likely due to influence from neighboring Mon and Tai languages (Matisoff 1991).
[Later: Another site says that Sqaw and Pwo are the only two that have a written language and these folks said they could write in their language. So that limits it down to those two. Someone in the office said their language was "Bakayaw" but that is in Thai.]