I have recently had an acrylic painting starting to buckle as it was drying. It had been painted on 100g paper which apparently was not the ideal surface to paint on.
My first reaction was to think about pasting it to a backing board for mounting. Fortunately I reconsidered and contacted my artist friends first.
I also came across an interesting approach by RB Anderson on YouTube
However, it was not really what I was looking for as I wanted a proper mount for my painting to go in a glass frame.
My painter friends advised against sticking the work down on an acid free board in case of air bubbles forming. Instead it was suggested to put it between two clean sheets of paper, weight it and leave it. At first I was reluctant to do so as I knew from past experience that acrylic paint can stick to glass when framed without a mount. So you either have to frame acrylics without glass like an oil painting or with a mount like a watercolour.
Finally I decided to brave it and put the painting under a pile of books not before I had put some clear plastic foil on it first to protect it. Every so often I had a look to made sure the foil did not stick to painting. It worked fine as long as the pile of books was not too heavy then it would begin to stick.
With all the parameters adjusted it turned out alright in the end flattening the painting enough for mounting. I do hope the customer will be happy with the result.