Hold the Option key and double-click on the word Background in your Layers Palette.
Make an accurate selection by the methods you're most comfortable with. Save it as an Alpha channel.
Add a Solid Color Adjustment Layer, and pick a red that's close in the Color Picker. Click OK.
Set the Adjustment Layer's Blending mode to Multiply.
Now, you can double-click on the color swatch in the A.L. and experiment with the hue and shade of the red in the Color Picker, watching it update in real time in your image. Adjust the color that comes up in the Color Picker to get the color you want. You can also tweak the opacity setting for the Adjustment layer if you want.
You can paint in the Adjustment Layer's mask if you need to fine tune the edges.
Watch out for the "almost black" areas. The Multiply blending mode may make them unnaturally dark. Mask them as well, or return and paint them out in the A.L. mask.
That's one way. There are others.
But it all starts with an accurate selection.
5 minutes or so worth of work (GIF "switchover" animation): <
http://www.pixentral.com/show.php?picture=1g4ncOXe6Xchn65hnk M07bDRytc0>