I love the "no time" excuse, because no matter how busy your day is, you always have a spare five minutes here and there: before a meeting starts, during your lunch hour, before you go to bed... Everyone has snippets of time, no matter how minimal, and you can use that time to write.
If you're just not in the mood to write, or are convinced that you have "no time" the real problem may be that you can't come up with a topic.
Here's what I do. If I'm not sure what I want to write (or think I can't write, for whatever reason), I write lists.
I might start a sentence with: "I have nothing to write about. I can't write about______ (a list of topics I can't write about)."
Or with: "I'm not in the mood to write, because ______ (a list of whatever is on my mind)."
Or with: "If I were enthusiastic about writing today, I could write ______ (a list of whatever normally enthuses me.)"
The point of lists is that they get me writing, and I can write wherever I happen to be, and whatever else is going on. I often write on my iPhone in the supermarket, in my car, and in front of the TV.
Basically, writing is a habit. If you write often enough, it will become a habit that's impossible to break. You'll find that you're always writing, no matter where you happen to be -- or how busy you feel you are.
I've just completed a new guide to article writing. You'll discover easy strategies which help you to write fast and easily -- and never run out of ideas again.