Carmelo Anthony Trying to Save Marriage with La La

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. We're told he insists La La's the only woman for him and has no plans to be with anyone else ... specifically not his alleged new baby mama.

Our sources say the 2 are still on friendly terms right now for their son -- so the relationship isn't toast yet -- but the pregnancy claim and his yet-to-be-determined NBA future are a lot of drama to handle.

Melo's just hoping for one more shot.