You can add your own button instead of using Google Sign-In buttonDo follwing things

Objective C Version

1)Add your own button into storyBoard

2)drag action into viewController

- (IBAction)googlePlusButtonTouchUpInside:(id)sender {     [GIDSignIn sharedInstance].delegate = self;     [GIDSignIn sharedInstance].uiDelegate = self;     [[GIDSignIn sharedInstance] signIn];  }

3)handle delegate methods

#pragma mark - Google SignIn Delegate

- (void)signInWillDispatch:(GIDSignIn *)signIn error:(NSError *)error {  }

// Present a view that prompts the user to sign in with Google

- (void)signIn:(GIDSignIn *)signIn presentViewController:(UIViewController *)viewController{    [self presentViewController:viewController animated:YES completion:nil];}

// Dismiss the "Sign in with Google" view

- (void)signIn:(GIDSignIn *)signIn dismissViewController:(UIViewController *)viewController {    [self dismissViewControllerAnimated:YES completion:nil];}

//completed sign In

- (void)signIn:(GIDSignIn *)signIn didSignInForUser:(GIDGoogleUser *)user     withError:(NSError *)error {//user signed in//get user data in "user" (GIDGoogleUser object)}

Swift 4 Version

In Swift make sure you have added briding header as the library is written in objective C

1)Add your own button into storyBoard

2)drag action into viewController

@IBAction func googlePlusButtonTouchUpInside(sender: AnyObject) {      GIDSignIn.sharedInstance().delegate=self      GIDSignIn.sharedInstance().uiDelegate=self      GIDSignIn.sharedInstance().signIn()} 

3)handle delegate methods

//MARK:Google SignIn Delegate

func signInWillDispatch(_ signIn: GIDSignIn!, error: Error!) {}

// Present a view that prompts the user to sign in with Google

func signIn(_ signIn: GIDSignIn!,    presentViewController viewController: UIViewController!) {  self.present(viewController, animated: true, completion: nil)}

// Dismiss the "Sign in with Google" view

func signIn(_ signIn: GIDSignIn!,    dismissViewController viewController: UIViewController!) {  self.dismiss(animated: true, completion: nil)}

//completed sign In

   public func signIn(_ signIn: GIDSignIn!, didSignInForUser user: GIDGoogleUser!,      withError error: Error!) {        if (error == nil) {          // Perform any operations on signed in user here.          let userId = user.userID                  // For client-side use only!          let idToken = user.authentication.idToken // Safe to send to the server          let fullName = user.profile.name          let givenName = user.profile.givenName          let familyName = user.profile.familyName          let email = user.profile.email          // ...        } else {          print("\(error.localized)")        }    }

Edit: Here is the reference/evidence for usage of custom button, Google Doc reference

In these examples, the view controller is a subclass of UIViewController. If, in your project, the class that implements GIDSignInUIDelegate is not a subclass of UIViewController, implement the signInWillDispatch:error:, signIn:presentViewController:, and signIn:dismissViewController: methods of the GIDSignInUIDelegate protocol. Also don't forget to set UI delegate GIDSignIn.sharedInstance()?.uiDelegate = self

Swift 3 Version

In Swift make sure you have added briding header as the library is written in objective C.

1. Add your own button into storyBoard

2. drag action into viewController

   @IBAction func googlePlusButtonTouchUpInside(sender: AnyObject) {      GIDSignIn.sharedInstance().signIn()} 

3. handle delegate methods

   //MARK:Google SignIn Delegate func signInWillDispatch(signIn: GIDSignIn!, error: NSError!) {  // myActivityIndicator.stopAnimating()    }// Present a view that prompts the user to sign in with Google   func sign(_ signIn: GIDSignIn!,              present viewController: UIViewController!) {        self.present(viewController, animated: true, completion: nil)    }// Dismiss the "Sign in with Google" view func sign(_ signIn: GIDSignIn!,              dismiss viewController: UIViewController!) {        self.dismiss(animated: true, completion: nil)    }//completed sign In    public func sign(_ signIn: GIDSignIn!, didSignInFor user: GIDGoogleUser!, withError error: Error!) {        if (error == nil) {      // Perform any operations on signed in user here.            let userId = user.userID                  // For client-side use only!           let idToken = user.authentication.idToken // Safe to send to the server            let fullName = user.profile.name           let givenName = user.profile.givenName           let familyName = user.profile.familyName           let email = user.profile.email          // ...        } else {            print("\(error.localizedDescription)")        }    }

For Swift 4: (This is working code Enjoy)

@IBAction func logimByGoogle(_ sender: Any) {    GIDSignIn.sharedInstance().delegate = self    GIDSignIn.sharedInstance().uiDelegate = self    GIDSignIn.sharedInstance().signIn()}//MARK:- Google Delegatefunc sign(inWillDispatch signIn: GIDSignIn!, error: Error!) {}func sign(_ signIn: GIDSignIn!,          present viewController: UIViewController!) {    self.present(viewController, animated: true, completion: nil)}public func sign(_ signIn: GIDSignIn!, didSignInFor user: GIDGoogleUser!,                   withError error: Error!) {    if (error == nil) {        // Perform any operations on signed in user here.        let userId = user.userID                  // For client-side use only!        let idToken = user.authentication.idToken // Safe to send to the server        let fullName = user.profile.name        let givenName = user.profile.givenName        let familyName = user.profile.familyName        let email = user.profile.email        // ...    } else {        print("\(error)")    }}