Here is how you can enable the Standard Copy/Paste:
TextView class has a definition:
boolean canPaste() {
    return (mText instanceof Editable
            && mEditor != null && mEditor.mKeyListener != null
            && getSelectionStart() >= 0
            && getSelectionEnd() >= 0
            && getClipboardManagerForUser().hasPrimaryClip());
}
Which can be bypassed using:
public static void enableCopyPaste(final TextView tv) {
    if(tv.getKeyListener()==null){
        tv.setKeyListener(new KeyListener(){
                @Override
                public void clearMetaKeyState(View p1, Editable p2, int p3) {
                    // unused
                }
                @Override
                public int getInputType() {
                    return tv.getInputType();
                }
                @Override
                public boolean onKeyDown(View p1, Editable p2, int p3, KeyEvent p4) {
                    // unused
                    return false;
                }
                @Override
                public boolean onKeyOther(View p1, Editable p2, KeyEvent p3) {
                    // unused
                    return false;
                }
                @Override
                public boolean onKeyUp(View p1, Editable p2, int p3, KeyEvent p4) {
                    // unused
                    return false;
                }
            });
    }
    tv.setTextIsSelectable(true);
    CharSequence mText = tv.getText();
    if(!(mText instanceof Editable)){
        tv.setText(mText,TextView.BufferType.EDITABLE);
    }
}
By calling:
enableCopyPaste(YOUR_TEXTVIEW);
Ps: It also enables Cut, Share etc