Hi, I have never seen one, certainly not a doped silica fibre. Do you want to transmit at around this ZDW; it's likely to suffer greatly from high macrobend sensitivity.
980-HP fiber has zero dispersion at ~1.8um. I used this fiber myself with 1.85um femtosecond laser and I was getting super broad spectrum at the output.
UHINA7 has normal dispersion up to 2.6um
UHINA4 has normal dispersion up to 2.4um. This fiber has been used previously to get normal dispersion at 2um (http://dx.doi.org/10.1063/1.4813108)
UHINA3 has normal dispersion up to 2.25um
UHINA1 has normal dispersion up to 2.15um
I think you could try GF4A fiber. I have never worked with this fiber but at least calculations show zero dispersion at 1.85um. I attached the dispersion curve for this fiber. All the above fiber available from Nufern. You can call them up and ask if they have any other high NA fiber.
You can also try to use SCF-UN-3/125-25 fiber from coractive.com, This one has zero dispersion at 2.04um. I also attached the dispersion curve for this fiber.
These fibers designed for 1-1.5um. When you use it for 2um make sure you don't have strong bends, otherwise, you will lose a lot of light.
I don't know of any commercial fibre designed specifically for zero dispersion at 1950 nm.
Have you looked at small core high index difference fibres such as Corning's HI 1060 fibre? This has high negative waveguide dispersion and may come close. It is designed for use at shorter wavelengths (980-1600 nm), but the high index difference improves mode confinement and bend resistance, compared with standard fibre. You would need to discover whether bend performance at 1950 nm is acceptable.
A high index difference with rather longer cut-off would be a better option. A fibre drawn to 125 micron diameter from a preform designed for 80 micron fibre would avoid the need for a custom preform, but could still be expensive if you only want a hundred metres.
What length of fibre do you need? At 1950 nm you are on the rising edge of the phonon absorption in silica. The Thorlabs web page has attenuation spectra for both silica and fluoride fibres. As Yurui points out, fluoride fibres may be an option, but I don't have dispersion data. The Klimentov paper linked below indicates how dispersion can be managed in this type of glass.