Yes, there are a very few tablets in cuneiform script where the language of the text is Aramaic. More common are Akkadian cuneiform tablets with Aramaic dockets written on their edge. The real question is, are recently discovered cuneiform tablets from Tal Mabtouh Sharqi in Syria written in the Aramaic language. Here’s what the Syrian Arab News Agency (SANA) article says about these tablets,
He [Director of Hasaka Antiquities Department, Abdul-Masih Baghdou] added that inside the level which dates back to the Ancient Babylonian Era, the expedition unearthed a number of the brick-made buildings and tombs including human skulls and funerary materials such as bronze-made tool and spear blades, in addition to Aramaic cuneiforms dating back to the Ancient Babylonian era.
What does “Ancient Babylonian Era” mean? As Jim Davila says, if it means the Old Babylonian period there is no way that these could be in Aramaic. And then there’s the question of what is meant by “Akkadian era” near the beginning of the article and “Modern (Assyrian Age)” in the last sentence of the piece. I’d guess that “Middle Assyrian Age” means Middle Assyrian Period but who knows? Period designations are often a mystery in SANA articles. Again, as Jim says, “But given SANA’s track record for garbling in these articles (see here, here, and here), I suspect the original announcement said something different, perhaps that Aramaic and cuneiform texts had been discovered.”
Whatever the language of these tablets, I hope they are published quickly because it is likely they are abnormally interesting.