You might want to write your own editor.
1. Use the default textarea, add a bar on top with two buttons bold italic.
2. Use jquery to capture the click event and add <b> tag or <i> tag
3. n°2 can be a bit tricky, you have to check if a word is marked, or if not, then enter <b>CURSOR</b>
4. When sending the post to the server, you need to make sure that it gets saved in format HTML.
Note: This solution assumes that the user knows the b and i tag and is not confused if they appear in the editor...
PS: It seems - as this is the second editor post I face today - that I should really finish the light weiht SCEditor implementation I started last year... (memo)