How to paint a room from bright pink to more neutral?

Get a good primer, while a little more expensive, its more likely to be a one-coat job, and cover the pink better

You will need two or maybe 3 coats of paint. The first coat should be a quality primer tinted silver to counteract the bright pink. Then proceed with your neutral color paint. Covering a bright color with cheap paint will not look good even after 4 coats. Due the prep work with the primer.

If you live in the USA, go to a big box store and get Oops! paint. $5 - $15 a gallon.

I would get a good quality paint and primer in one...there are a few on the market that state one coat coverage, you still might have to do two coats, but paint isn't super expensive if you're applying it yourself

If you are going to go through the trouble of painting a room, my vote is to do it right from the get go for a long lasting finish. Wash the walls with TSP, let dry then prime (do not skip this step), with a good primer like Kilz or Zinsser, then paint of your choice. Then paint trim, doors.

First, use a good primer to neutralize the color. Then paint with a good quality paint.

Both Lowes and Home Depot accept paint back that customers either don't like or bought too much of. Oops! paint is in the paint departments. Just ask where it's at and look through the different paints. Have them open it up to make sure it's not full of water (unfortunately this happens from not nice people). They'll shake it up for you and you're off to finish up this project and on to the next. Good luck.

I've mixed similar tones in a 5 gallon bucket and gotten all I need for a big job. I buy the sample paints, the one gallons in all the sheens, both indoor and outdoor. As long as it's latex you can do this. I always save some for touch ups because this is one-of-a-kind paint, but it's a way to get a job done on the cheap, cheap, cheap.