Can I download a new program to a Silicon Labs C8051F311 with a JTAG programmer?
From Section 20 of the datasheet


  C8051F31x devices include an on-chip
  Silicon Labs 2-Wire (C2) debug
  interface to allow Flash program- ming
  and in-system debugging with the
  production part installed in the end
  application. The C2 interface uses a
  clock signal (C2CK) and a
  bi-directional C2 data signal (C2D) to
  transfer information between the
  device and a host system. See the C2
  Interface Specification for details on
  the C2 protocol.


So, yes, sounds like you need a special (non JTAG) programmer.

Here's one, it's $35.