BUG: conversion a JSON field descriptor into pandas type for deprecated offsets frequency 'M' (#55581)

* correct convert_json_field_to_pandas_type

* fix pre-commit errors

* correct def convert_json_field_to_pandas_type in case freq_n>1

* remove print

* add parameterization to the test

* replace the regex with to_offset

Author: natmokval

pandas/io/json/_table_schema.py

@@ -15,6 +15,7 @@
 from pandas._libs import lib
 from pandas._libs.json import ujson_loads
 from pandas._libs.tslibs import timezones
+from pandas._libs.tslibs.dtypes import freq_to_period_freqstr
 from pandas.util._exceptions import find_stack_level
 
 from pandas.core.dtypes.base import _registry as registry
@@ -34,6 +35,8 @@
 from pandas import DataFrame
 import pandas.core.common as com
 
+from pandas.tseries.frequencies import to_offset
+
 if TYPE_CHECKING:
     from pandas._typing import (
         DtypeObj,
@@ -207,8 +210,12 @@ def convert_json_field_to_pandas_type(field) -> str | CategoricalDtype:
         if field.get("tz"):
             return f"datetime64[ns, {field['tz']}]"
         elif field.get("freq"):
+            # GH#9586 rename frequency M to ME for offsets
+            offset = to_offset(field["freq"])
+            freq_n, freq_name = offset.n, offset.name
+            freq = freq_to_period_freqstr(freq_n, freq_name)
             # GH#47747 using datetime over period to minimize the change surface
-            return f"period[{field['freq']}]"
+            return f"period[{freq}]"
         else:
             return "datetime64[ns]"
     elif typ == "any":

pandas/tests/io/json/test_json_table_schema.py

@@ -845,3 +845,14 @@ def test_read_json_orient_table_old_schema_version(self):
         expected = DataFrame({"a": [1, 2.0, "s"]})
         result = pd.read_json(StringIO(df_json), orient="table")
         tm.assert_frame_equal(expected, result)
+
+    @pytest.mark.parametrize("freq", ["M", "2M"])
+    def test_read_json_table_orient_period_depr_freq(self, freq, recwarn):
+        # GH#9586
+        df = DataFrame(
+            {"ints": [1, 2]},
+            index=pd.PeriodIndex(["2020-01", "2020-06"], freq=freq),
+        )
+        out = df.to_json(orient="table")
+        result = pd.read_json(out, orient="table")
+        tm.assert_frame_equal(df, result)