I used Project GC to rank the countries based on number of caches ever published in a country which gave me a list of all countries that are counted as countries by HQ. In that list, there are six countries that currently do not have a geocache: Somalia, Bouvet Island, Tuvalu, Heard Island and McDonald Islands, Cocos (Keeling) Islands, and North Korea.
Ireland still does not have a souvenir though it does have regional souvenirs. This is inconsistent with how HQ has country and regional souvenirs for United States, Germany, Canada, and Australia.
The countries that rank the highest in caches ever published that do not have souvenirs are: Serbia (61), Afghanistan (65), Guadeloupe (66), Martinique (79), Svalbard and Jan Mayen Islands (113), French Guiana (119), Sark (181), and Mayotte (196).
The countries that rank the lowest in caches ever published that have souvenirs are South Georgia and the South Sandwich Islands (239), British Indian Ocean Territory (236), Sierra Leone (235), and Liberia (234).
Below are the countries without souvenirs. I personally am waiting on souvenirs for the highlighted ones.