requery() updates a Cursor, not a CursorAdapter. As you say, it has been deprecated, and its replacement is:
oldCursor = myCursorAdapter.swapCursor(newCursor); // hands you back oldCursor
or:
myCursorAdapter.changeCursor(newCursor); // automatically closes old Cursor
myCursorAdapter.notifyDataSetChanged() notifies the ListView that the data set has changed, and it should refresh itself
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