This was taken from Wikipedia's Southern Hemisphere article. I eliminated all of those in South America and those that are obviously not in the east. Atleast 80% of these should be in both. Not a perfect answer but one nonetheless.
Africa
Entirely
- Angola
- Botswana
- Burundi
- Comoros
- Lesotho
- Madagascar
- Malawi
- Mauritius
- Mozambique
- Namibia
- Rwanda
- Seychelles
- South Africa
- Swaziland
- Tanzania
- Zambia
- Zimbabwe
Mostly
- Democratic Republic of the Congo
- Gabon
- Republic of the Congo
Partly
- Equatorial Guinea
- Kenya
- Somalia
- São Tomé and Príncipe
- Uganda
Asia
Entirely
Mostly
Partly
Australia
Entirely
- Australia
- Indonesia
- Papua New Guinea
Pacific Ocean
- American Samoa (USA)
- Cook Islands (New Zealand)
- Easter Island (Chile)
- Fiji
- French Polynesia (including Tahiti) (France)
- Galápagos Islands (Ecuador)
- Jarvis Island (USA)
- Juan Fernández Islands (Chile)
- Nauru
- Territory of New Caledonia and Dependencies (France)
- New Zealand
- Niue (New Zealand)
- Kermadec Islands (New Zealand)
- Pitcairn Islands (United Kingdom)
- Samoa
- Solomon Islands
- Swains Island (USA, claimed by Tokelau)
- Tokelau (New Zealand)
- Tonga
- Tuvalu
- Vanuatu
- Wallis and Futuna (France)
Partly
Indian Ocean
- British Indian Ocean Territory (United Kingdom)
- Mayotte (France)
- Réunion (France)
Southern Ocean
- Antarctic and sub-Antarctic islands
- Bouvet Island (Norway)
- Kerguelen Islands (France)
- New Zealand Sub-Antarctic Islands (New Zealand)
- Saint Paul Island and Amsterdam Island (France)
- South Georgia and the South Sandwich Islands (United Kingdom, claimed by Argentina)
- South Orkney Islands (Antarctic Treaty signatories
