Raj I did what you suggested and it works.
In my application, when the down key is pressed, the text should start scrolling. For this reason I'm using a timer and the image is repainted every time. To be more precise, and as you suggested, the text is painted on the mutable image at a different y coordinate, thus giving the effect of the scrolling text.
The problem is (and it is a big problem for the application that I am trying to create) the "scrolling" is not smooth at all. I need to make a prompting application and the scrolling appears to be too jerky. When I was painting the entire text on a single mutable image and then just clipping the image, the scrolling effect was much smoother.
What I do is
at the beginning and then, at each interval of the timer
im = com.sun.lwuit.Image.createImage(m_screenWidth, m_screenHeight);
y is the position where the string is drawn. If I want to scroll down, y is negative.
// Draw a filled (black) rectangle
g.fillRect(0, 0, im.getWidth(), im.getHeight());
// Specify the current Font
// Draw text in white
int fontHeight = m_currentFont.getHeight();
s = nextLine().trim();
g.drawString(s, x, y);
y += fontHeight;
hasMoreLines() and nextLine() are functions that I found online and are used to wrap the text.