We know of no organised tours to Swaziland.
We know of no birding guides in Swaziland.
We know of no trip reports.
Travel to Swaziland is best visited from South Africa via the 11 border posts on its western border. Generally speaking, cars hired from the major hire companies in South Africa can be driven into Swaziland, hence this is the most effective way to visit this country. Roads are good in Swaziland, but look out for pedestrians and livestock.
You can also travel by air from Johannesburg.
Guidebooks, travel companies and websites provide the advice one needs, but key points warrant repetition here: (1) be aware of the risk of malaria and seek current advice, sleep in a sealed tent or under a net and take prophylaxis as recommended; (2) always ensure you have sufficient water and some method of purification (even if this comprises a pot and a campfire for boiling); (3) do not underestimate the danger of being in the sun for too long, ensure you use sun-block, drink plenty of water and wear a hat; (4) be aware of the risk of AIDS (note that Swaziland has the highest incidence of AIDS of any country in the world); (5) ensure that you take a reasonably-equipped first-aid pack with you including supplies of hypodermic and suturing needles. See the following 2 websites or your own embassy website for the latest safety and travel information: US Travel and UK FCO.