I don't think there is one to be honest. Unless people are shipping Satoshi and Gou... Everyone is kinda at a standstill... Amourshipping is at the same level as pearl and pokeshipping... Lots of hope but little to talk about.
I would guess that Amourshipping is the most popular ship in the anime since it has the most hints. None of the Alola ships seem all that popular while older ships with actual hints like Pokeshipping are considered old and outdated.
Interesting how there seems to be ship tease with Gou and Satoshi in the anime right now even though they are both boys. Although I doubt that it will amount to anything if a heterosexual ship like Amourshipping only got an off-screen kiss and no real confession scene.
SM didn't really have a big ship, some shipped Ash/Lillie like usual, or Lillie/Mallow. Amourshipping has died down a bit now that we're 3 years removed from XY and Serena might never show up again, so support for it has slowed down.
And besides that people just continually like the older ships they grew up with, but again, most older fans have left the pokemon fandom, so there's not much activity. When all the original fans are now close to 30 years old or older, obviously you're not going to see them in the fandom anymore. Almost everyone from the early/mid 2000's, like 2003-2012 or so, is pretty much gone.