Is there a way to instruct search engines (especially Google Search) that a website is meant to be accessed only on desktop/laptop? One of my websites is not displaying properly on smartphones but displaying okay on desktops/laptops.
All new websites must be mobile friendly. So, if it's a new site, you are out of luck.
I think that it is less work to start off correctly with a responsive design than to fix it later. It will take much more time to fix it later.
However, if you must, then I would suggest that you use different URLs for mobile and non-mobile and point them to a single page with a friendly message such as
Mobile Support Coming Soon, and suffer Google's displeasure. In some cases, it may refuse to show the results.
I found this on developers.google
Create a mobile-friendly site
If you haven't already, create a mobile-friendly website so your users visiting your site through a mobile phone can have a stellar experience. There are three configurations you can choose from to create a mobile-friendly site:
Responsive design: Serves the same HTML code on the same URL regardless of the users' device (for example, desktop, tablet, mobile, non-visual browser), but can display the content differently based on the screen size. Google recommends Responsive Web Design because it's the easiest design pattern to implement and maintain.
Dynamic serving: Uses the same URL regardless of device. This configuration relies on user-agent sniffing and the Vary: user-agent HTTP response header to serve a different version of the HTML to different devices.
Separate URLs: Serves different HTML to each device, and on separate URLs. Like dynamic serving, this configuration relies on the user-agent and Vary HTTP headers to redirect users to the device-appropriate version of the site.
The contents of this guide only apply to dynamic serving and separate URL configurations. In case of responsive design, the content and the metadata are the same on the mobile and desktop version of the pages.