This virtual slot 31 is your CI card. And this is the number that you might need. I would think that you would need the part number:
MAS-7500CI= MAS-7500CI=, 7500 CHASSIS INTERFACE SPARE or
RSP7000CI
Here is a link describing replacement:
http://www.cisco.com/univercd/cc/td/doc/product/core/cis7000/frus/25627ci.htm
Here is the output of the show diag you were referring to:
Slot 31 (virtual):
EEPROM format version 1
7000 Chassis Interface, HW rev 1.00, board revision A0
Serial number: 03142519 Part number: 73-1769-02
Test history: 0x00 RMA number: 00-00-00
Flags: cisco 7000 board
EEPROM contents (hex):
0x20: 01 19 01 00 00 2F F3 77 49 06 E9 02 00 00 00 00
0x30: 50 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
Hope this helps,
Don