All the runners in Platinum either are part Flying or have Levitate.
A better choice would be Wobbuffet, as earlier suggested.
The battle will take place over many fights. Paralyze them (I'd suggest Sleep, but it's not permanent), False Swipe them, then when they're down to minimum health and status-afflicted, keep out the tank with Shadow Tag and throw Ultra Balls (or, if at night, Dusk Balls for better chances). It will take many Balls to catch them. THAT'S HOW LEGENDARIES (minus Dialga and Palkia) WORK. THEY ARE SUPPOSED TO TAKE UP 20+ BALLS.
On a side note, have at least 30 Ultra Balls, 10 Timer Balls, and maybe 20 Dusk Balls if you plan to hunt at night.
And to the person initially asking, you're offering Cresselia? Which is gotten THE EXACT SAME WAY as the birds? Why can't you just capture the birds the way you got Cresselia?