It could be accomplished by specifying AnchorId property for TaxonomyWebTaggingControl control.
This property allows to specify ID of parent Term for any valid value in control.
Assume we have the following structure for the countries:
- the first level is the continents
- the second level is the countries

If we initialize TaxonomyWebTaggingControl control and specify for AnchorId Europe Term Id value
/// <summary>
/// Initializing TaxonomyWebTaggingControl control
/// </summary>
/// <param name="countryControl"> </param>
/// <param name="session"></param>
/// <param name="continentTerm"></param>
private void InitCountriesControl(TaxonomyWebTaggingControl countryControl, TaxonomySession session, Term continentTerm)
{
countryControl.SSPList = continentTerm.TermStore.Id.ToString();
countryControl.AnchorId = continentTerm.Id;
countryControl.TermSetList = continentTerm.TermSet.Id.ToString();
}
then only countries for selected continent will be displayed

For more details and how to implement Country picker based on Countries term set please see my blog - Using SharePoint TaxonomyWebTaggingControl control: specifying parent terms