What is the problem with the hint of green? I often try to remind people that the wall will fill up and the furniture will take presidents of the room with such light paint. idk if it matters but all those rugs have a blue-green tone in them except from what I can tell the all pink and yellow one.

If you are doing gender-neutral room I wold goo with the bottom right

Maybe you need to add to and or adjust the lighting in the room. Different bulbs can also make a difference. Although, I do agree with R L Relocation that maybe the green is kind of ok.. even nice, perhaps. And I agree that the rug on bottom right might be a good option, to complement it.

When the time comes to ditch the broadloom, replace it with a hard surface. Even vinyl plank would be fine under a large rug. Have a serious look at North African rugs: winter white with fine black line designs.

I like either of the two right bottom rugs, since they both have a hint of green with the blue/pink. The top middle could also work. They would look better than the pale pinks and yellow with light wood furniture. The wall color looks fine, and will read as just white once everything else is in.