All the birds of the Solomon Islands are illustrated and discussed in Chris Doughty, Nicholas Day, and Andrew Plant’s Birds of the Solomons, Vanuatu & New Caledonia (ISBN 978-0-7136-4690-0). It is the first field guide for the region it covers, and it illustrates many species for the first time. It contains range maps and descriptions of voice, etc.
I do not have field experience in the Solomons (though I expect to gain some during 2008), but birders who do say that there are some problems with the way certain species are illustrated and represented on the maps. This is something to be aware of, but you still need the guide.
Ernst Mayr and Jared Diamond’s joint project, The Birds of Northern Melanesia: Speciation, Ecology, and Biogeography (ISBN 978-0-19-514170-2), is a reference work for the Bismarck and Solomon islands. Besides the topics mentioned in the title, the book contains color plates illustrating some (less than half) of the region’s species and regional forms, and it contains distribution information. A thorough review was published in The Auk. It wouldn’t make a good substitute for a field guide, but it would be a helpful companion and reference.