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In >=SQL Server 2012, the ReorientObject() method should accomplish this. For <SQL Server 2012, below is an alternative method.

For an existing SQL geography @g, code below will extract the points and re-create a polygon with points (vertices) in reverse order:
(NOTE 1: works for simple polygons, not for multipolygons or polygons with rings/centroids)
(NOTE 2: using SRID 4326 (WGS 84) coordinate system)

--For existing geography @g
DECLARE @GeometryText varchar(max), @ReversedPolygon geography
DECLARE @GeometryType varchar(20) = 'POLYGON', @Count int
SET @Count = @g.STNumPoints()
WHILE @Count > 0
BEGIN
    SET @GeometryText = @GeometryText + CONVERT(varchar(30),CONVERT(decimal(12,8),@g.STPointN(@Count).Long)) + ' ' + CONVERT(varchar(30),CONVERT(decimal(12,8),@g.STPointN(@Count).Lat))
    SET @Count = @Count - 1
    IF @Count > 0 SET @GeometryText = @GeometryText + ','
END
SET @GeometryText = @GeometryType +'((' + @GeometryText + '))'
SET @ReversedPolygon = geography::STGeomFromText(@GeometryText, 4326); 

In >=SQL Server 2012, the ReorientObject() method should accomplish this. For <SQL Server 2012, below is an alternative method.

For an existing SQL geography, @g, the code below will extract the points and re-create a polygon with points (vertices) in reverse order:

-- For existing geography @g
DECLARE @GeometryText varchar(max), @ReversedPolygon geography
DECLARE @GeometryType varchar(20) = 'POLYGON', @Count int
SET @Count = @g.STNumPoints()
WHILE @Count > 0
BEGIN
    SET @GeometryText = @GeometryText + CONVERT(varchar(30),CONVERT(decimal(12,8),@g.STPointN(@Count).Long)) + ' ' + CONVERT(varchar(30),CONVERT(decimal(12,8),@g.STPointN(@Count).Lat))
    SET @Count = @Count - 1
    IF @Count > 0 SET @GeometryText = @GeometryText + ','
END
SET @GeometryText = @GeometryType +'((' + @GeometryText + '))'
SET @ReversedPolygon = geography::STGeomFromText(@GeometryText, 4326);

• It only works for simple polygons, not for multipolygons or polygons with rings/centroids.
• It uses the SRID 4326 (WGS 84) coordinate system. (See last line.)

For an existing SQL geography @g, below is code that will extract the points and re-create a polygon with points (vertices) in reverse order:
(NOTE 1: works for simple polygons, not for multipolygons or polygons with rings/centroids)
(NOTE 2: using SRID 4326 (WGS 84) coordinate system)

--For existing geography @g
DECLARE @GeometryText varchar(max), @ReversedPolygon geography
DECLARE @GeometryType varchar(20) = 'POLYGON', @Count int
SET @Count = @g.STNumPoints()
WHILE @Count > 0
BEGIN
    SET @GeometryText = @GeometryText + CONVERT(varchar(30),CONVERT(decimal(12,8),@g.STPointN(@Count).Long)) + ' ' + CONVERT(varchar(30),CONVERT(decimal(12,8),@g.STPointN(@Count).Lat))
    SET @Count = @Count - 1
    IF @Count > 0 SET @GeometryText = @GeometryText + ','
END
SET @GeometryText = @GeometryType +'((' + @GeometryText + '))'
SET @ReversedPolygon = geography::STGeomFromText(@GeometryText, 4326); 

In >=SQL Server 2012, the ReorientObject() method should accomplish this. For <SQL Server 2012, below is an alternative method.

For an existing SQL geography @g, code below will extract the points and re-create a polygon with points (vertices) in reverse order:
(NOTE 1: works for simple polygons, not for multipolygons or polygons with rings/centroids)
(NOTE 2: using SRID 4326 (WGS 84) coordinate system)

--For existing geography @g
DECLARE @GeometryText varchar(max), @ReversedPolygon geography
DECLARE @GeometryType varchar(20) = 'POLYGON', @Count int
SET @Count = @g.STNumPoints()
WHILE @Count > 0
BEGIN
    SET @GeometryText = @GeometryText + CONVERT(varchar(30),CONVERT(decimal(12,8),@g.STPointN(@Count).Long)) + ' ' + CONVERT(varchar(30),CONVERT(decimal(12,8),@g.STPointN(@Count).Lat))
    SET @Count = @Count - 1
    IF @Count > 0 SET @GeometryText = @GeometryText + ','
END
SET @GeometryText = @GeometryType +'((' + @GeometryText + '))'
SET @ReversedPolygon = geography::STGeomFromText(@GeometryText, 4326); 

For an existing geography @g, below is code that will extract the points and re-create a polygon with points (vertices) in reverse order:

 (NOTE: using SRID 4326 (WGS 84) coordinate system)

DECLARE @GeometryText varchar(max), @ReversedPolygon geography
DECLARE @GeometryType varchar(20) = 'POLYGON', @Count int
SET @Count = @g.STNumPoints()
WHILE @Count > 0
BEGIN
    SET @GeometryText = @GeometryText + CONVERT(varchar(30),CONVERT(decimal(12,8),@g.STPointN(@Count).Long)) + ' ' + CONVERT(varchar(30),CONVERT(decimal(12,8),@g.STPointN(@Count).Lat))
    SET @Count = @Count - 1
    IF @Count > 0 SET @GeometryText = @GeometryText + ','
END
SET @GeometryText = @GeometryType +'((' + @GeometryText + '))'
SET @ReversedPolygon = geography::STGeomFromText(@GeometryText, 4326); 

For an existing SQL geography @g, below is code that will extract the points and re-create a polygon with points (vertices) in reverse order:
(NOTE 1: works for simple polygons, not for multipolygons or polygons with rings/centroids)
(NOTE 2: using SRID 4326 (WGS 84) coordinate system)

--For existing geography @g
DECLARE @GeometryText varchar(max), @ReversedPolygon geography
DECLARE @GeometryType varchar(20) = 'POLYGON', @Count int
SET @Count = @g.STNumPoints()
WHILE @Count > 0
BEGIN
    SET @GeometryText = @GeometryText + CONVERT(varchar(30),CONVERT(decimal(12,8),@g.STPointN(@Count).Long)) + ' ' + CONVERT(varchar(30),CONVERT(decimal(12,8),@g.STPointN(@Count).Lat))
    SET @Count = @Count - 1
    IF @Count > 0 SET @GeometryText = @GeometryText + ','
END
SET @GeometryText = @GeometryType +'((' + @GeometryText + '))'
SET @ReversedPolygon = geography::STGeomFromText(@GeometryText, 4326);