Note: Untested...

UPS 
DB9 male connector
DB9 female connector
PC

PC Side
Pin #1  Data Carrier Detect     CD 
Pin #2  Receive Data            RD or RX or RXD 
Pin #3  Transmitted Data        TD or TX or TXD 
Pin #4  Data Terminal Ready     DTR 
Pin #5  Signal Ground           GND 
Pin #6  Data Set Ready          DSR 
Pin #7  Request To Send         RTS 
Pin #8  Clear To Send           CTS 
Pin #9  Ring Indicator          RI 

UPS Side
Pin #1  Shutdown (rs232) input
Pin #2  Line fail (rs232) output
Pin #3  Active low Line fail output
Pin #4  Common ground
Pin #5  Active low Low Battery output
Pin #6  Active high Line fail output
Pin #7  Remote UPS On/Off input (smart only)
Pin #8  Unregulated +24DC output (smart only)
Pin #9  Chassis ground

We connect UPS#2 [Line fail] to PC#1 [CD], so that when we lose power,
carrier detect goes high (I think CD is active low on RS232).  We connect
UPS#5 [Battery Low] to PC#8 [CTS], so that CTS will go low when we have
battery low. We connect UPS#1 [Shutdown] to PC#3 [TX] so that we can
completely control the signal level. We connect a 4.7KOhm resistor from
UPS#2 to UPS#5, so that we pull up the battery fail pin when it is not
active. This assumes that the line fail output will be active when the
battery fails.

UPS#2 [PF]      ---> PC#1 [CD]
 |
 > 4.7KOhm
 <
 |
UPS#5 [LB]      ---> PC#8 [CTS]
UPS#1 [SD]      <--- PC#3 [TX]
UPS#4 [GND]     ---- PC#5 [GND]

Parts
1. DB 9 to rj45 male kit
1. DB 9 to rj45 female kit
1. rj45 cable [we have it]
1. 4.7KOhm resistor
1. soldering iron and solder for resistor
1. breakout-box or voltmeter for debugging [el cheapo kind]