Can a couple of permanent residents adopt their 2 grandchildren after their mother died in a country different from the United States?

First, I am so sorry for your loss.

I am assuming the children are not in the United States and are not U.S. citizens. If this is so, this is an international adoption. It is possible
to adopt internationally, but you need to talk to an agency who is Hague certified. To find a list of these agencies in the United States go to:
http://adoption.state.gov/hague_convention/agency_accreditation/agency_s...

In addition, I would suggest that you visit this web site that is maintained by the US Dept. of Health and Human Services. It provides detailed
information about Intercountry adoption from Hague Convention and Non-Hague Convention Countries:
http://www.childwelfare.gov/pubs/factsheets/hague.cfm