Carmelo Anthony's playing right up to the final buzzer ... doing everything he can to win La La back and keep their marriage from ending in divorce.
Sources close to the couple tell us ... Melo's been sending his estranged wife texts telling her he's still in love and doesn't want her to leave him. We're told he's apologized over and over, and is begging for another chance by asking her on dates or to go on vacation together.
Carmelo's also been doing something he never used to do -- liking her posts on social media.