If the value of the textarea is already set (e.g. it is set programmatically by a script or hand coded into the page) you could try wrapping the words to be coloured in spans with class names in order to apply color CSS.
If you can give us more information about your intent and the structure of the page, a more detailed answer should be possible :)
Update You can't put code into a textarea ><
If you're coloring text that must be typed by visitors, i.e. a
<textarea> must be used, consider using a
<div> element that the text they type into the textarea is copied into, and the
<span> elements can be used in the
<div>, a similar setup to how comments are typed/previewed here