Citizens of the following countries do not need visas for visits up to 90 days.
Andorra, Argentina, Austria, Australia, Bahamas, Barbados, Belgium, Botswana, Bosnia-Herzegovina, Brazil, Brunei, Canada, Cayman Islands, Croatia, Cyprus, Chile, Czech Republic, Denmark, Dominica, Estonia, Finland, Faeroe Islands, Falkland Islands, France, Futuna Islands, Gambia, Germany, Ghana, Greece, Grenada, Greenland, Guyana, Hungary, Ireland, Israel, Italy, Jamaica, Japan, Kenya, Kuwait, Lactivia, Lesotho, Liechtenstein, Lithuania, Luxembourg, Malawi, Malaysia, Malta, Maldives, Madagasgar, Mauritius, Monaco, Mozambique, Namibia, Nauru, Netherlands, New Zealand, Norway, Papua New Guinea, Poland, Portugal, Russia, San Marino, Serbia, Seychelles, Sierra Leone, Singapore, Slovenia, South Africa, South Korea, Spain, Sweden, Switzerland, Svalbard and Jan Mayen Islands, Taiwan, Tanzania, Tonga, Trinidad and Tobago, Turkey, Tuvalu, Uganda, Ukrain, United States of America, Uruguay, Uganda, United Kingdom, United Arab Emirates, United Nations Passport Holders, Vanuatu, Vatican City, Zambia and Zimbabwe
Visas are fairly easy to arrange and cost around US$10 for a 3 month visa.
Swaziland Visa Information and embassies
Swaziland government and entry requirements