Get the default timezone for a country (via CultureInfo)

May not be exactly what you are looking for, but try this: http://msdn.microsoft.com/en-us/library/system.timezoneinfo.aspx

To get a specific time zone:

TimeZoneInfo tZone = TimeZoneInfo.FindSystemTimeZoneById("E. Australia Standard Time");

To see the available zones:

ReadOnlyCollection<TimeZoneInfo> zones = TimeZoneInfo.GetSystemTimeZones();

foreach (TimeZoneInfo zone in zones)
{
     Console.WriteLine(zone.Id);
}

As identified in the comments of the question, you aren't going to be able to get a single time zone for each country. There are just too many cases of countries that have multiple time zones.

What you can do is filter the list of standard IANA/Olson time zones down to those available within a specific country.

One way to do this in C# is with Noda Time:

IEnumerable<string> zoneIds = TzdbDateTimeZoneSource.Default.ZoneLocations
    .Where(x => x.CountryCode == countryCode)
    .Select(x => x.ZoneId);

Pass a two-digit ISO-3166 country code, such as "AU" for Australia. The results are:

"Australia/Lord_Howe",
"Australia/Hobart",
"Australia/Currie",
"Australia/Melbourne",
"Australia/Sydney",
"Australia/Broken_Hill",
"Australia/Brisbane",
"Australia/Lindeman",
"Australia/Adelaide",
"Australia/Darwin",
"Australia/Perth",
"Australia/Eucla"

And if for some reason you'd like Windows time zone identifiers that you can use with the TimeZoneInfo object, Noda Time can map those too:

var source = TzdbDateTimeZoneSource.Default;
IEnumerable<string> windowsZoneIds = source.ZoneLocations
    .Where(x => x.CountryCode == countryCode)
    .Select(tz => source.WindowsMapping.MapZones
        .FirstOrDefault(x => x.TzdbIds.Contains(
                             source.CanonicalIdMap.First(y => y.Value == tz.ZoneId).Key)))
    .Where(x => x != null)
    .Select(x => x.WindowsId)
    .Distinct()

Again, called with "AU" for Australia returns:

"Tasmania Standard Time",
"AUS Eastern Standard Time",
"Cen. Australia Standard Time",
"E. Australia Standard Time",
"AUS Central Standard Time",
"W. Australia Standard Time"

If you're wondering about how reliable this data is, the country to tzid mapping is part of the IANA time zone database itself, in the zone.tab file. The IANA to Windows mapping data comes from the Unicode CLDR supplemental data. It doesn't get any closer to "official" than that.