Here's the problem: What color are we replacing? We can say "pink", but there are actually a range of colors in that image that make our brains say "pink", and they range from a pink so light that it's nearly white, down to a fairly dark magenta. By mapping them to a GIF space, we can see a table of colors, and get a better understanding of what we're dealing with. Anything not black, white or neutral gray is something we'll have to contend with and attempt to convert to the new color:
So, when we replace the original color with the new color, what we're really going to be doing is replacing the old hues with the chosen red hue -
with the equivalent amounts of saturation and brightness of that new hue found in the old hue it's replacing. That bolded part is the important thing to remember.
Now that we understand that aspect of it, let's see what happens.
First, we need to know exactly what the replacement color is. Using the eyedropper tool, we find that the red they've chosen is a hue of 0 degrees, saturation of 99%, and a brightness of 84%. Now we simply go to the foreground color and click on it, dial in those exact settings, and we have the exact color we need on our palette.
Now I'll go to the replacement brush, zoom in on the image so I can clearly choose a pink/magenta starting point, and get ready to replace the old colors with the new. I'm using a brush size of 35 pixels and fairly hard at 95%. My brush is set up to use a crosshair target in the middle so I know exactly where I'm about to sample. The replacement brush is set to Hue, Discontiguous, a tolerance of 90% and Anti-alias is checked.
Now I click on a pink/magenta pixel on a layer copy of the original image so that I don't destroy the original in case I have to start all over, and paint over the whole image with the replacement hue of the chosen red. Here's what we get:
It has faithfully done it's job. The more saturated or brighter the original pink/magenta, the the more saturated or brighter the new chosen red hue is.
But is that what the client is expecting? Probably not, because in their minds they see the original as "pink", as though it's a single contiguous color, and it's simply not. Problem is, most of the original hues were nowhere near the levels of saturation and brightness the new chosen red hue is, so only a few pixels in the image are going to actually use that bright saturated red the clients have chosen.
Well, what can we do about it? If we re-color everything in the original image that has any color to it at all with the new red, we're just going to get blotches of red all over the place, with no nuance of detail (and I'll bet you got that in your many tries already). That's certainly not what the client will want.
We can add a hue saturation adjustment layer to punch it up more, and that might get us closer. Doing that and increasing the saturation to +60, we get this:
Maybe that's closer to what the client is expecting? It's more saturated, and the most saturated parts are definitely the chosen red the client wants, but it's already starting to fall apart on us as it blotches up from rendering a wider range of hues into a contiguous bright saturated red, and there's still not all that much of it, so it doesn't "look" like the chosen red the client is probably expecting.
Okay, just for giggles, let's see what happens when we take it up to +80:
Well, now it's starting to fall apart pretty quickly, as we further expand those "blotches of color" areas by mapping even more hues to the bright saturated red, and it's only going to get worse if we keep going. The further we go, the more nuance we lose and the details simply disappear, which is pretty ugly and 180 degrees out from the calming effect the Buddha image is likely intended to convey.
So, now that we have a much better understanding of the problem, how do we solve it? I honestly don't know a way to do it convincingly.
Maybe someone else has a way to make this work in a way that the client actually expects in their mind's eye and thinks is possible, but I have my doubts because of the nature of what color replacement actually is. I'd sure be interested to learn the method involved if someone else can do it though.
Best of luck.