In the attachment you will find nfc.golfu.so which is the firmware for HTC Desire C with NFC (phone model PL01110). I get it from RUU_GOLF_U_ICS_40A_H3G_UK_1.45.771.3_Radio_10.11.9 8.09H_1.06.98.13M2_release_266089_signed.exe that you can find on the net.
I upload firmware here because I have spend 3 weeks to get it working with [STABLE][ROM][4.1.2][JZO54K] CyanogenMod10 | BUILD #3.
On this rom, we see the NFC option but it can not enable it and we get the error hw_get_module() failed with logcat and the option stick unchecked.
With the attachement to this post, NFC is working (at least with JZO54K CM10 build#3), see logcat :
I/NfcService( 477): Enabling NFCSo what to do do with this nfc.golfu.so ?
D/NFCJNI ( 477): Start Initialization
I/dalvikvm( 315): Jit: resizing JitTable from 4096 to 8192
D/NFCJNI ( 477): NFC capabilities: HAL = 8150100, FW = a76d0c, HW = 620003, Model = 10, HCI = 1, Full_FW = 109, Rev = 12, FW Update Info = 0
D/NFCJNI ( 477): phLibNfc_SE_GetSecureElementList()
D/NFCJNI ( 477):
D/NFCJNI ( 477): > Number of Secure Element(s) : 1
D/NFCJNI ( 477): phLibNfc_SE_GetSecureElementList(): SMX detected, handle=0xabcdef
D/NFCJNI ( 477): phLibNfc_SE_SetMode() returned 0x000d[NFCSTATUS_PENDING]
I/NFCJNI ( 477): NFC Initialized
Uncompress file nfc.golfu.zip and you will get nfc.golfu.so
Put the file (nfc.golfu.so) on /system/lib/hw/ on your phone.
chmod 644 /system/lib/hw/nfc.golfu.so
Then reboot your phone and now, you can check NFC option and you can use it (at least with phone having NFC AND rom having NFC enabled)