Overlaying a UIImage with a color?

You will want to clip the context to an image mask and then fill with a solid color:

- (void)drawRect:(CGRect)rect
{
    CGRect bounds = [self bounds];
    [[UIColor blackColor] set];
    CGContextRef context = UIGraphicsGetCurrentContext();
    CGContextClipToMask(context, bounds, [myImage CGImage]);
    CGContextFillRect(context, bounds);
}

Note: myImage should be an instance variable that contains an UIImage. I'm not sure whether it takes the mask from the alpha channel or the intensity so try both.

So, to sum up all the answers into one here's the drop-in method that works perfectly from iOS 6 all the way up to iOS 11 with all kinds of images and icons:

+ (UIImage *)filledImageFrom:(UIImage *)source withColor:(UIColor *)color{

    // begin a new image context, to draw our colored image onto with the right scale
    UIGraphicsBeginImageContextWithOptions(source.size, NO, [UIScreen mainScreen].scale);

    // get a reference to that context we created
    CGContextRef context = UIGraphicsGetCurrentContext();

    // set the fill color
    [color setFill];

    // translate/flip the graphics context (for transforming from CG* coords to UI* coords
    CGContextTranslateCTM(context, 0, source.size.height);
    CGContextScaleCTM(context, 1.0, -1.0);

    CGContextSetBlendMode(context, kCGBlendModeColorBurn);
    CGRect rect = CGRectMake(0, 0, source.size.width, source.size.height);
    CGContextDrawImage(context, rect, source.CGImage);

    CGContextSetBlendMode(context, kCGBlendModeSourceIn);
    CGContextAddRect(context, rect);
    CGContextDrawPath(context,kCGPathFill);

    // generate a new UIImage from the graphics context we drew onto
    UIImage *coloredImg = UIGraphicsGetImageFromCurrentImageContext();
    UIGraphicsEndImageContext();

    //return the color-burned image
    return coloredImg;
}

Update: Swift 3 version

func filledImage(source: UIImage, fillColor: UIColor) -> UIImage {

    UIGraphicsBeginImageContextWithOptions(source.size, false, UIScreen.main.scale)

    let context = UIGraphicsGetCurrentContext()
    fillColor.setFill()

    context!.translateBy(x: 0, y: source.size.height)
    context!.scaleBy(x: 1.0, y: -1.0)

    context!.setBlendMode(CGBlendMode.colorBurn)
    let rect = CGRect(x: 0, y: 0, width: source.size.width, height: source.size.height)
    context!.draw(source.cgImage!, in: rect)

    context!.setBlendMode(CGBlendMode.sourceIn)
    context!.addRect(rect)
    context!.drawPath(using: CGPathDrawingMode.fill)

    let coloredImg : UIImage = UIGraphicsGetImageFromCurrentImageContext()!
    UIGraphicsEndImageContext()

    return coloredImg
}