Adding country list control to my webpart using code behind

You can use Kentico's API, i believe it's CountryInfoProvider.GetCountries()

You can append other stuff, such as .OrderBy("CountryDisplayName"), etc.

just foreach through these and fill up your repeater. Something like below, note may be syntax errors, just free handing it.

foreach(CountryInfo Country in CountryInfoProvider.GetCountries()) {
    ddlMyDropDown.Items.Add(new ListItem(Country.CountryName, Country.TwoLetterCode));
}