From the iPhone Application Programming Guide
However, you can programmatically
display the keyboard for an editable
text view by calling that view’s
becomeFirstResponder method. Calling
this method makes the target view the
first responder and begins the editing
process just as if the user had tapped
on the view.
So to show the keyboard programmatically,
[textView becomeFirstResponder];
However, the keyboard will never show if the textView is not editable.
The purpose of showing the keyboard is to allow editing. I assume you just don't want the keyboard to appear when the user taps the text view. In this case, you can enable editable programmatically when the button is tapped.
-(IBAction) yourButtonClick
{
myText.editable = YES;
[myText becomeFirstResponder];
}
Then in the UITextViewDelegate, disable editable when the user finishes editing.
- (void)textViewDidEndEditing:(UITextView *)textView {
textView.editable = NO;
}