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For some reason there are no review links, so I'll review in this message.
Include/datetime.h
+typedef struct {
..
+} _datetimemodulestate;
Names exposed in public headers (datetime.h is a public header) should start with Py or _Py. Other offenders include _datetimemodule_state, _datetimemodule, _datetimemodulestate_global.
I don't think these names need to be defined in the header file at all. 
+typedef struct {
+ /* Forward declarations. */
+ PyObject *PyDateTime_DateType;
+ PyObject *PyDateTime_DateTimeType;
...
These are not forward declarations anymore. There is no need for PyDateTime_ prefix. Use names from PyDateTime_CAPI struct.