以下のコードを試してください。NewViewController を表示したいポイントから以下のメソッドを呼び出すだけです。必要なことは、NewViewcOntroller の View Frame の OriginY を変更することだけです。
-(void)displayNewVC
{
YourNewViewController *newVC = [[YourNewViewController alloc] init];
CGFloat originY = -450;//set originY as you want to display newViewController from the Top to bottom with animation
//initially set originY out of the Frame of CurrentViewcontroller
newVC.view.frame = CGRectMake(orginX, originY, newVC.view.frame.size.width, newVC.view.frame.size.height);
/*Display View With Animation*/
originY = 300;
[UIView animateWithDuration:.3 animations:^{
//set new originY as you want.
newVC.view.frame = CGRectMake(orginX, originY, newVC.view.frame.size.width, newVC.view.frame.size.height);
} completion:NULL];
[currentViewController.view addSubview:newVC.view];
}