diff --git a/sparse/numba_backend/_coo/core.py b/sparse/numba_backend/_coo/core.py
index fb39aaab..3f01cd3e 100644
--- a/sparse/numba_backend/_coo/core.py
+++ b/sparse/numba_backend/_coo/core.py
@@ -1556,7 +1556,9 @@ def __binsparse__(self) -> tuple[dict, list[np.ndarray]]:
                             },
                         }
                     }
-                },
+                }
+                if self.ndim != 2
+                else "COOR",
                 "shape": list(self.shape),
                 "number_of_stored_values": self.nnz,
                 "data_types": {