So most of my recommendations do have a triangle, BUT they're not true competitors and have no real chance. It sounds like you're more-so trying to avoid second-lead syndrome. But if it is the actual existence of ANY triangle of any kind you are trying to avoid, I do have two recommendations in there that have no second-lead.
The Princess' Man - There was never any competition with the second-lead. Her heart was always with the main guy and never wavers.
City Hunter - Again, no competition with the second lead.
Full House (Thai) - I found the second-leads suuuuuuuper annoying, definitely not worthy of pulling you away from the main pair. So if you don't mind annoying second-leads. I recommend it. haha.
Healer - This one has NO second-lead vying for her affection.
Pinocchio - No real competition from the second-lead.
Scent of a Woman - The second-lead is a dear friend. Obviously he loves her, but she never wavers.
Secret - The second-lead is pure evil. So.....no competition and not someone anyone would want to root for.
Splash Splash LOVE - There is NO second-lead. Just pure cuteness.
The Master's Sun - No competition with the second lead.
Witch's Romance - So you end up pretty much hating her ex and he's no competition to the noona romance. BUT she does get pretty angsty about their relationship and gets back together with him for a brief time. Again, no competition in the viewer's heart, but still.
You Who Came From the Stars - She never likes the second-lead, there's no real competition.
