How to generate tinymce in ajax generated text area

If you show me your code, I can help you better. However, you should be able to call this function and pass the ID of the Ajax-generated TextArea to it.

//add this to your Ajax callback that generates the TextArea
//replace with the Id of the new textarea
var myTextArea = document.getElementById("MyNewTextArea"); 
generateTinyMCE(myTextArea);

//Add this function to your script tag
function generateTinyMCE(id) {
 if (!tinyMCE.get(id))
   tinyMCE.execCommand('mceAddControl', false, id);
 else
   tinyMCE.execCommand('mceRemoveControl', false, id);
}