Not knowing the country I can only guess it to be from one of the following:
Chile, mintage 173,000, value in a condition of fine $1.25
El Salvador, mintage 1,000,000, value in a condition of fine $2.25
Honduras, mintage 168,000, value in a condition of very good $1.50
Nicaragua, mintage 750,000, value in a condition of fine $2
Philippines, mintage 4,540,000, value in a condition of fine $0.75
I'm pretty sure these are the only countries that issued a centavo in 1919. Nothing rare but there are a couple of low mintage coins (Chile & Honduras) where I'd keep the coin just for the unusual factor. As far as reading material for that many countries I'd have to recommend the Krause Publication "Standard Catalog of World Coins" (see our recommended reading page). It's a bit pricey but you migh pick up a used copy on the cheap or you could just post your questions here and I can lookup info for you.
Ken
P.S. If you can't read the country name then checkout this site http://worldcoingallery.com/ and see if any of the pics from the countries above look like your coin.