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You are unlikely to get penalized for something that small but it is against Googles TOS.

"Make the site for the user"

Just put it in the footer in the copyright text.

Whatever you do Dylan, don't do that!

That will cause your client's site to get penalized and you're treading on very thin ice.

This is an old, but well-known way to hide links and will likely get your client's site banned quicker than you can blink.

There was a company years and years ago (an SEO company - I hate how companies like this give us bad names) who would create a 1x1 pixel on every last one of their clients sites that contained backlinks. Not only did the SEO companies site get banned (and sued as well if I remember correctly) but every last one of their clients sites were banned as well.

You don't want to step into that hot water.

Instead, I would ask your client what their purpose is for not having any links on their site. It seems like they're digging their own grave already. Show them how important links are to their overall success online, and if that fails, just ask if you could add a link to their sitemap, their footer (as Easy Cash suggested) or anyplace else on their site.

In the future, when you work on clients sites, I would recommend that in your contract you place a section that states you have the right to place a small logo at the bottom of their site that says "site designed by..."