There is a short list of dye ink compatible inkjet media in my SpectrumViz application. Among them swellable media from Felix Schoeller and Kodak. Kodak wide format media are now distributed by BMG, address is in the paper distributor links of the SpectrumViz page.
There still are desktop dye ink printers in the Canon, HP, Epson catalogs and the better dyes; Claria, Vivera dye, Canon's (Chromolife?) should be used with compatible papers to get at least some of longevity claimed for those inks. Whether papers from the other brands can replace the HP qualities I do not know. Many CAD wide format models from HP and Canon still have at least dye inks for gloss printing, matte black ink can be pigment though, check the compatible gloss photo papers for that category of printers, from OcÚ as well.
For the FujiFilm, Noritsu and Epson dry minilabs a clone of the Claria dye ink is used (origin is most likely FujiFilm chemicals, even for Epson). The dry minilab printers use sheets or rolls with a maximum of 30 cm wide. Consider them at least compatible with Claria dye ink that claims better longevity than usual dye/paper combinations. So check dry minilab suppliers too for consumables. Canon has a dry minilab dye model ready but I doubt it runs anywhere now so it will be hard to get the media from that source. I got some samples on the Photokina; Canon DreamLabo qualities.
If longevity is no issue then there is quite some development happening in papers for fast web inkjet printing, matte to high gloss. Felix Schoeller and more companies. Collected some dual sided samples on the Photokina and the image quality is good. Not RC paper though. Large rolls and pallet deliveries of sheets but maybe a distributor could take the risk of confection for a smaller market.
Dye is not dead yet.
Met vriendelijke groet, Ernsthttp://www.pigment-print.com/spectralplots/spectrumviz_1.htm
490+ inkjet paper white spectral plots, November 2012:
rearranged categories, Sihl Masterclass papers added.