Shipwreck Singer has the ability:
1U: Target creature an opponent controls attacks this turn if able.
When can I activate this ability?
e.g. My opponent has a Manaweft Sliver. I say "attack if able" at the beginning of the draw step of my opponent. Can he now use the mana ability or does he have to honor my attack order and can no longer use its mana ability?
"Attacks this turn if able" means: when the Attack phase comes around, if that creature is able to attack, it must. That doesn't come with an obligation to leave it able to attack, though, and your opponent may rightly wish to do something that leaves that creature unable to attack.
Your opponent can use Manaweft's Sliver ability. Then, when the Attack phase comes around, Manaweft Sliver won't be able to attack, and won't do so.
He does have to attack you when he's able to. But when your opponent taps for mana, the creature stays tapped (tapping is part of the cost and cannot be interrupted), therefore it's not able to attack in his attack phase.
Even if your opponent activates the creata mana-ability in his main phase (later than your ability was activated), he still won't be able to attack. He's allowed to do that to prevent his sliver(s) from attacking.
