長男 (chou nan) is a fairly common word for the oldest son. I've never heard it used to mean "beloved" for a non-eldest son though.
My dictionary says 愛息 (aisoku) is normally used for other people's sons. There is nothing else wrong with it. You are going to find it difficult finding a term in japanese because normally you don't speak respectfully about family members unless they "rank higher" than you and you are addressing them directly.
One possibility is 愛し子 (itoshigo) or literally 最愛の息子 (saiai no musuko)
What you will notice in all these is the character for love "愛" which you could use by itself just as a reminder.
Sorry for your loss by the way.