Swaziland is now as Eswatini.
Citizens of the following countries do not need visas for visits up to 90 days.
Andorra, Anguilla, Antigua and Barbuda, Argentina, Australia, Austria, Bahamas, Barbados, Belgium, Belize, Bermuda, Bosnia-Herzegovina, Botswana, Brazil, British National (Overseas), British Virgin Islands, Brunei, Canada, Cayman Islands, Channel Islands, Chile, Cook Islands, Croatia, Cyprus, Czech Republic, Denmark, Dominica, Estonia, Eswatini (formerly Swaziland), Faeroe Islands, Falkland Islands, Finland, France, Gambia, Germany, Ghana, Gibraltar, Greece, Greenland, Grenada, Guyana, Hungary, Ireland, Israel, Italy, Jamaica, Japan, Kenya, Kuwait, Latvia, Lesotho, Lithuania, Luxembourg, Madagascar, Malawi, Malaysia, Maldives, Malta, Mauritius, Monaco, Montserrat, Mozambique, Namibia, Nauru, Netherlands, New Zealand, Niue, Norfolk Island, Northern Mariana Island, Norway, Occupied Palestinian Territory, Papua New Guinea, Pitcairn, Poland, Portugal, Qatar, Republic of Korea, Reunion, Russia, Saint Helena, Saint Lucia, Saint Pierre and Miquelon, San Marino, Serbia and Montenegro, Seychelles, Sierra Leone, Singapore, Slovakia, Slovenia, Solomon Islands, South Africa, Spain, Svalbard and Jan Mayen Islands, Sweden, Switzerland, Taiwan (Republic of China), Tanzania, Timor-Leste, Tokelau, Tonga, Trinidad and Tobago, Turkey, Turks and Caicos Islands, Tuvalu, Uganda, Ukraine, United Kingdom, United Nations Passport Holders, United States of America, Uruguay, Vanuatu, Vatican City, Wallis and Futuna Islands, Western Samoa, Zambia and Zimbabwe.
Everyone else will need to arrange a visa before arrival.
Visas are fairly easy to arrange and cost around US$10 for 3 months
Eswatini Visa Information and embassies
Swaziland government and entry requirements