Most of the important Syriac MSS come from before the 7th/8th century and all the families of the text were created before then as well. The two earliest represent what is called the Old Syriac family of texts and the MSS themselves date from late 4th, early 5th century, but preserve a text type that is much earlier.
After that there is the Peshitta family of MSS, which we have MSS from 463/464 AD and moving back into the 5th centuries from there. It is not sure just how early this text was produced but some trace it back to Rabbula, which is around the 5th centruy or so.
In fact, because of the Christological controversies, there were two more recensions of the text in Syriac, the Harklean and Philoxennian, which occurred in the early 7th century (615 AD, I think - the good news is that this is colophon dated, which is the most reliable).
So, long story short, all of the text families in existence from the Syriac tradition were created before the 7/8th centuries. The text itself in Syriac is actually very stable compared to most other traditions, probably due to the Semitic nature of the Scribes, and so the "official" Syriac version, the Peshitta, was established and stable throughout the Church well before the 6/7th century.