What shifters are compatible with shimano 9-speed?
According to the Wikipedia page, the following groupset variations were specifically 9-speed:


Dura-Ace 7700 (1996-2002)
Ultegra 6500 (1997-2004)
105 5500 (dates unknown)
Tiagra before 4600 (before 2011)
Sora 3400 (2012-)


As far as other components go, it seems that as long as the cassette, chain and shifters match then the groupset should work. All Shimano rear derailleurs (excluding early Dura-Ace) have the same shift ratio, so they should work so long as the derailleur has enough travel capacity - use one rated for the same or higher number of gears than in your cassette.