I have been very disappointed since finding out my new S9 phone won't let me have delegate sounds for text messages from my favorite contacts. It was because of the custom sounds for text notifications that made me choose an S9 over an iPhone. I hope they bring it back!
There is an another option if you dont have update for app yet. Download and install apk manually from Apkmirror. Just download the newest one and give it a try. It works for me on S7/S7 Edge, S8/S8+ and also S9/S9+. Let me know if it helps. Regards.
Edit: ON S8 22.214.171.124 works aswell.
I am on verison 126.96.36.199 of the Samsung messaging and it lets me. I opened the app and then pressed on a conversation between me and a friend then the options button (three dots in a line) in the top right hand corner. It will then bring down an options menu. There is a option right at the top called 'conversation settings', which underneath will have 'notifications' and then 'default' in blue. I clicked on this and it loaded up a second screen allowing me to change from the default to custom. I could then choose the tone I wanted.
I have the Note8 and my latest message update is showing to be up to date and is 188.8.131.52 and it still isn't giving me the option to set individual text tones for my contacts. 😡