I don't find 'only Son' or 'one and only Son' acceptable translations for monogenes for the simple reason that they are not true. 'For you are all sons of God through faith in Christ Jesus' (Galatians 3:26).
The difference between us and the Lord Jesus, of course is that, unlike Him, we are sons by adoption (Romans 8:15 etc.). So the translation 'unique Son' is not without merit. But the reason that He is unique is that He is the only begotten Son (John 1:14, 18).
'We believe in .......one Lord Jesus Christ, the only begotten Son of God, begotten of His Father before all worlds, God of God, Light of Light, very God of very God, begotten, not made, being of one substance with the Father; by whom all things were made' [Nicene Creed]
'The Son is eternally begotten of the Father' [Baptist 1689 Confession]
The argument is made that because Luke 7:12; 8:42; 9:38 use the word monogenes for an only child, it cannot mean 'only begotten.' But in each of those verses, that is precisely what it means. Also, adoption was much more widespread in ancient times than it is today. If a man had no sons, or only one, he would often adopt a nephew or other male child to ensure the succession of his line. The most famous examples are the emperors Augustus and Tiberius. Augustus, when he was a youngster named Octavian, was adopted by Julius Caesar, and Tiberius was adopted by Augustus. So Jairus, for example, might well have adopted a son, but his daughter was his only begotten child.