You need to break the column data into two columns and then use the average function by converting the date into float.
Following is the example:
DECLARE @test_date TABLE (dt datetime)
INSERT INTO @test_date VALUES (GETDATE() + 1)
INSERT INTO @test_date VALUES (GETDATE() + 2)
INSERT INTO @test_date VALUES (GETDATE() + 3)
SELECT CONVERT(char(8),CAST(AVG(CAST(dt AS FLOAT) - FLOOR(CAST(dt AS FLOAT))) AS datetime),108) FROM @test_date