How can I change the color of the UITabBar top border by creating a UIImage programmatically?

You've pretty much answered your own question. You can do the same thing with your UITabBar as you did with your UINavigationBar. If you want to change the shadow image (i.e. the "top border"), then you have to change the background image. Straight from Apple:

The custom shadow image for the tab bar. This attribute is ignored if the tab bar does not also have a custom background image. To set this attribute programmatically, use the shadowImage property.

In your own question you seem to be aware of this:

the only way to change the color of the top border is to set the background image (320x49, with pixel line at top)

Except that it's not the background image that has a line at the top. You just have to set the background image to anything, then you can set the shadow image to your preference.

If you open up the simple "tabbed application" template within Xcode, you'll find that adding these two lines of codes (and your UIImage extension code) indeed work:

// White background with red border on top
UITabBar.appearance().backgroundImage = UIImage.colorForNavBar(.whiteColor())
UITabBar.appearance().shadowImage = UIImage.colorForNavBar(.redColor())

Here is the Swift 3 solution:

extension UIImage {
    class func colorForNavBar(color: UIColor) -> UIImage {
        let rect = CGRect(x: 0.0, y: 0.0, width: 1.0, height: 1.0)
        //    Or if you need a thinner border :
        //    let rect = CGRect(x: 0.0, y: 0.0, width: 1.0, height: 0.5)
        UIGraphicsBeginImageContext(rect.size)
        let context = UIGraphicsGetCurrentContext()

        context!.setFillColor(color.cgColor)
        context!.fill(rect)

        let image = UIGraphicsGetImageFromCurrentImageContext()
        UIGraphicsEndImageContext()

        return image!
    }
}

used with the code above in the viewDidLoad of the UITabBarController

UITabBar.appearance().backgroundImage = UIImage.colorForNavBar(color: .white)
UITabBar.appearance().shadowImage = UIImage.colorForNavBar(color: .red)

You need to provide an different image for UINavigationBar.appearance().backgroundImage.

For example:

UINavigationBar.appearance().backgroundImage = UIImage.colorForNavBar(.blackColor())
UINavigationBar.appearance().shadowImage = UIImage.colorForNavBar(.redColor())