Citizens of the following countries do not need visas for visits up to 90 days.

Andorra, Anguilla, Antiqua and Barbuda, Argentina, Austria, Australia, Azerbaijan, Bahamas, Barbados, Belize, Belgium, Bermuda, Botswana, Bosnia-Herzegovina, Brazil, British Virgin Islands, Brunei, Burkina Faso, Caicos Islands, Canada, Cayman Islands, Channel Islands, Cook Islands, Croatia, Cyprus, Republic of China on Taiwan, Chile, Czech Republic, Denmark, Dominica, Estonia, Finland, Faeroe Islands, Falkland Islands, France, Futuna Islands, Gambia, Germany, Ghana, Gibraltar, Greece, Grenada, Greenland, Guyana, Hungary, Ireland, Israel, Italy, Jan Mayen Islands, Jamaica, Japan, Kenya, Kuwait, Lactivia, Lesotho, Liechtenstein, Lithuania, Luxembourg, Malawi, Malaysia, Malta, Maldives, Madagasgar, Mauritius, Monaco, Mozambique, Montserrat, Namibia, Nauru, Netherlands, New Zealand, Niue, Norway, Norfolik Island, Northern Mariana Island, Palestinian Occupied Territory, Papua New Guinea, Pitcairn, Poland, Portugal, Reunion, Russia, Saint Helena, Saint Lucia, Saint Pierre and Miquelon, San Marino, Serbia and Montenegro, Seychelles, Sierra Leone, Singapore, Solomon Islands, Slovenia, Slovakia, South Africa, South Korea, Spain, Sweden, Switzerland, Svalbard and Jan Mayen Islands, Tanzania, Timor-Leste, Tokelau, Tonga, Trinidad and Tobago, Turkey, Turks and Caicos Islands, Tuvalu, Uganda, Ukrain, United States of America, Uruguay, Uganda, United Kingdom, United Arab Emirates, United Nations Passport Holders, Vanuatu, Vatican City, Wallis and Futuna Islands, Western Samoa, Yugoslavia, Zambia and Zimbabwe

Visas are fairly easy to arrange and cost  around US$10 for 3 months

Swaziland Visa Information and embassies

Swaziland government and entry requirements