Hi,
This may be a bit difficult.
To get started, what you can do is separate the different parts of the control. In this case, you should separate it into a scrollbar, a textbox and the text itself.
You can store the text in a string array (or arraylist), and display only the needed portion. Then, you need to manually handle scrolling -calculate the right size of the scroll bar, the amount of text to be scrolled each time and so on. You will have to place more text on the textbox than actually visible, so that some original scrolling ability will be kept, allowing you to add text on the direction of scroll, delete text on the opposite direction, handle the currently displayed line (as when your delete from the beginning it will probably scroll automatically) and hide the original scrollbar. The issue of adding text and deleting it in the background is complicated and should be thought into deep details. For example, you wouldn't like the interface to hang when you scroll fast, so you might need to do some threading operations.
I would recommend that you limit the development version to a small limit of text (for example 300 lines) so that you can test it more easily.