We investigate the operation of holmium-doped fibre amplifiers (HDFAs) in the 2.1 µm spectral region. For the first time we demonstrate a diode-pumped HDFA. This amplifier provides a peak gain of 25 dB at 2040 nm with a 15 dB gain window spanning the wavelength range 2030 - 2100 nm with an external noise figure (NF) of 4-6 dB. We also compare the operation of HDFAs when pumped at 1950 nm and 2008 nm. The 1950 nm pumped HDFA provides 41 dB peak gain at 2060 nm with 15 dB of gain spanning the wavelength range 2050 - 2120 nm and an external NF of 7-10 dB. By pumping at the longer wavelength of 2008 nm the gain bandwidth of the amplifier is shifted to longer wavelengths and using this architecture a HDFA was demonstrated with a peak gain of 39 dB at 2090 nm and 15 dB of gain spanning the wavelength range 2050 - 2150 nm. The external NF over this wavelength range was 8-14 dB.