There is an easy and straightforward solution to this problem:
Turn on Team Attack.
Any doubles tournament should have team attack on anyway, and this is just one of the reasons why.
If by some chance you were having trouble with team attack still on, first learn how to deal with spammers in 1v1s. Shield, reflect, dodge, or jump as you approach. If using a reflector, go in front of your ally, of course. If spot dodging and shielding, it shouldn't matter how many players are involved defensively. Once you get it down pat, no amount of spamming should faze you unless you aren't expecting it. (In which case it's not spamming, it's a legitimate long range attack.)
With team attack on, precious few pairs of good spamming options can be used in tandem, so that you only have to defend against one player's spam. And the other opponent's attempts to interrupt your approach are limited by his teammate's spamming, too.