Talk to the press about them. Stating that you think they are a good player, show alot of promise etc. That only sometimes works though. Other than that i dont think there is another way.
If its ure players, praise performances, criticize underperformances, learning new moves (if they dont want to dont insist), make them tutor someone (again, if the kid doesnt want to dont insist). Also make ure team win titles and have good performances.
If its someone u want to buy, then walden covered it already.
Lots and Lots of private chats seems to help a player like me and get me on their favoured personal. Other than that I found by doing extremely well in the league or cup competition also helps this