How would I tint an image programmatically on iOS?

In iOS7, they've introduced tintColor property on UIImageView and renderingMode on UIImage. To tint an UIImage on iOS7, all you have to do is:

UIImageView* imageView = …
UIImage* originalImage = …
UIImage* imageForRendering = [originalImage imageWithRenderingMode:UIImageRenderingModeAlwaysTemplate];
imageView.image = imageForRendering;
imageView.tintColor = [UIColor redColor]; // or any color you want to tint it with

First you'll want to subclass UIImageView and override the drawRect method. Your class needs a UIColor property (let's call it overlayColor) to hold the blend color and a custom setter that forces a redraw when the color changes. Something like this:

- (void) setOverlayColor:(UIColor *)newColor {
   if (overlayColor)
     [overlayColor release];

   overlayColor = [newColor retain];
   [self setNeedsDisplay]; // fires off drawRect each time color changes
}

In the drawRect method you'll want to draw the image first then overlay it with a rectangle filled with the color you want along with the proper blending mode, something like this:

- (void) drawRect:(CGRect)area
{
  CGContextRef context = UIGraphicsGetCurrentContext();
  CGContextSaveGState(context);

  // Draw picture first
  //
  CGContextDrawImage(context, self.frame, self.image.CGImage);

  // Blend mode could be any of CGBlendMode values. Now draw filled rectangle
  // over top of image.
  //
  CGContextSetBlendMode (context, kCGBlendModeMultiply);
  CGContextSetFillColor(context, CGColorGetComponents(self.overlayColor.CGColor));      
  CGContextFillRect (context, self.bounds);
  CGContextRestoreGState(context);
}

Ordinarily to optimize the drawing you would restrict the actual drawing to only the area passed in to drawRect, but since the background image has to be redrawn each time the color changes it's likely the whole thing will need refreshing.

To use it create an instance of the object then set the image property (inherited from UIImageView) to the picture and overlayColor to a UIColor value (the blend levels can be adjusted by changing the alpha value of the color you pass down).