This just popped into my head yesterday. Your mission, should you choose to accept it, is to construct a scenario where the largest religious denomination in the United States in 2009 is "Eastern Rite Catholic."
Two initial ideas come to my mind:
1) A TL where all or at least a great part of Orthodox Europe converts to Eastern Catholicism
2) Much, much greater Ukrainian and Catholic Arab immigration to the USA early on, replacing or at least overshadowing the Irish/Italian/German influxes that formed most of OTL's Catholic American population.