I think NYX Pinky will pair better with Pink Pigeon. I use NYX Plush Red for Party Parrot. I prefer liners that are slightly darker than the lipstick when I wear bright colors. It helps better with the transition from the skin to the lipstick. I fill my lips with Plush Red then apply Party Parrot over it. It's still bright, but not "why did she leave the house looking like that" bright. If I feel like toning it down a bit more, I use a brown pencil close to my skin tone to outline my lips on top of the lipstick. For me, it's usually MAC Cork or NYX Toast. I use other brown liners too, but nothing too dark like MAC Chestnut. It will just kill the brightness of the lipstick too much. I then go back and reapply Party Parrot to the center of my lips to brighten it back up a little.
My goal is to keep the color as true as possible, but to make it more wearable for my skin tone. If I want to manipulate the color, then I normally use a purple lip pencil. Here are the NYX dupes that I think are the closest to the MAC purple lip pencils in my stash.
MAC Magenta = NYX Purple Rain
MAC Plum = NYX Never
MAC Currant NYX Currant / NYX Deep Purple (they're close, but still off)
MAC Vino = NYX Plum
MAC Nightmoth = NYX Y2K