Find information about research grant calls from around the world I am based at a southern European university where little local research funding is available. Other than Horizon 2020, how can I find out about programs designed to sponsor research in any country?
Here are several options:


Research Raven. This site focuses on calls for papers and conferences, some of which include funding. Most of the listings relate to medical and healthcare related opportunities. 
ScanGrants. This is a sister site to Research Raven, and is "designed to facilitate the search for funding sources to enhance individual and community health....
Funding sources most frequently listed here include those of private foundations, corporations, businesses, and not-for profit organizations. Finding and listing less traditional funding opportunities is also a priority. Federal and state funding sources are typically not included on ScanGrants™ because they are readily available on other sites." Their listing are somewhat US-centric, though. 
European Research Council. I am not very familiar with ERC.  The website states "ERC grants are open to researchers of any nationality in the world, any scientific field, any age. ". It seems well worth checking out. 
The Wenner-Gran Foundation suppports collaborative research with a focus on anthropology. You have not specified your field, but depending on your circumstance this may be worth looking at. 
Conference Alerts will provide you with a free alert system for conferences in your field, for any or all countries. Although this is not a grant-finding/listing service, the individual conferences may have funding available to you. 
Finally, this Google search may bring some useful results.