Seems the problem was elsewhere and injecting it like any other class seems to work fine. For those who are wondering:

My Image class constructor:

use Illuminate\Config\Repository as Config;

class Image {
    public function __construct(
        Config $config
    ) {
        $this->config = $config;
    }
}

My ImageSpec.php:

function let(\Illuminate\Config\Repository $config)
{
    $this->beConstructedWith($config);
}

function it_is_initializable()
{
    $this->shouldHaveType('Acme\Images\Image');
}

Yes, it works if you leave it at that. However if you add another function to the image class like this:

function isAccepted(){
    return in_array($this->type, $this->config->get('accepted_types'));
}

I don't think it will work in this case. Or you will get weird results at best.