Could build one - shallow water (that might be the hard bit), artificial base then a thick layer of imported rock/soil. :)
Unfortunately, Tonga claimed the island and kicked them out.
Generally, some nation will come and take it from you. Wolf Hilbertz developed an technique to electrically accrete limestone out of sea water and was using it to build a micronation, but it was almost certain that it would be seized by Mauritius when it broke surface.
http://en.wikipedia.org/wiki/Saya_de_Malha_Bank#Artificial_i...