Add this function to you JavaScript:
function textarea_to_tinymce(id){
if ( typeof( tinyMCE ) == "object" && typeof( tinyMCE.execCommand ) == "function" ) {
tinyMCE.execCommand('mceAddControl', false, id);
}
}
then when you create the textarea dynamically call it and pass the textarea’s id to it.
Just make sure TinyMCE is loaded on that page before or it won’t work.