Does Google love co.nr domain names? Or they dont even look at them?

Have you notices sites with co.nr domain name in google indexing???

it is not a real domain tld

a company owns the domain co.nr and what you get is a subdomain on their site.

So you can never "own" your name and any promotion you do will be lost when you decide to move. But the SEs should index it. One problem that can occur though is if one of the sub domains get used for spam mailing many others may become affected by the filters of some ISPs

google or other search engines will index co.nr domains/subdomains
if they have enough incoming links.
but the greatest problem with them is,
they show your site in frames.
if you wish you can see the source of your co.nr site.
and search engines cant index content in frames.

now what happens is they will index only the co.nr page title and description only and not your site content.