Solution
The following table lists which pins are accessible through each BNC-2110 connected to the M Series Device: 
Connector block 1 (PCI-6259 Connector 0)| BNC-2110 |   PCI-6259 | 
|---|
| P0.0 / DIO 0 | P0.0 (pin 52) | 
| P0.1 / DIO 1 | P0.1 (pin 17) | 
| P0.2 / DIO 2 | P0.2 (pin 49) | 
| P0.3 / DIO 3 | P0.3 (pin 47) | 
| P0.4 / DIO 4 | P0.4 (pin 19) | 
| P0.5 / DIO 5 | P0.5 (pin 51) | 
| P0.6 / DIO 6 | P0.6 (pin 16) | 
| P0.7 / DIO 7 | P0.7 (pin 48) | 
| PFI 0 / AI START / TRIG 1 | PFI 0 / P1.0 (pin 11) | 
| PFI 1 | PFI 1 / P1.1 (pin 10) | 
| PFI 2 | PFI 2 / P1.2 (pin 43) | 
| PFI 3 | PFI 3 / P1.3 (pin 42) | 
| PFI 4 | PFI 4 / P1.4 (pin 41) | 
| PFI 5 | PFI 5 / P1.5 (pin 6) | 
| PFI 6 | PFI 6 / P1.6 (pin 5) | 
| PFI 7 | PFI 7 / P1.7 (pin 38) | 
| PFI 8 | PFI 8 / P2.0 (pin 37) | 
| PFI 9 | PFI 9 / P2.1 (pin 3) | 
| EXTSTRB | PFI 10 / P2.2 (pin 45) | 
| AI HOLD / SCANCLK | PFI 11 / P2.3(pin 46) | 
| CTR 0 OUT | PFI 12 / P2.4 (pin 2) | 
| CTR 1 OUT | PFI 13 / P2.5 (pin 40) | 
| F OUT / FRQ OUT | PFI 14 / P2.6 (pin 1) | 
| not accessible | PFI 15 / P2.7 (pin 39) | 
 
Connector block 2 (PCI-6259 Connector 1)| BNC-2110 | PCI-6259 | 
|---|
| P0.1 / DIO 1 | P0.9 (pin 17) | 
| P0.2 / DIO 2 | P0.10 (pin 49) | 
| P0.3 / DIO 3 | P0.11(pin 47) | 
| P0.4 / DIO 4 | P0.12 (pin 19) | 
| P0.5 / DIO 5 | P0.13 (pin 51) | 
| P0.6 / DIO 6 | P0.14 (pin 16) | 
| P0.7 / DIO 7 | P0.15 (pin 48) | 
| PFI 0 / AI START / TRIG 1 | P0.16 (pin 11) | 
| PFI 1 | P0.17(pin 10) | 
| PFI 2 | P0.18 (pin 43) | 
| PFI 3 | P0.19 (pin 42) | 
| PFI 4 | P0.20 (pin 41) | 
| PFI 5 | P0.21 (pin 6) | 
| PFI 6 | P0.22 (pin 5) | 
| PFI 7 | P0.23 (pin 38) | 
| PFI 8 | P0.24 (pin 37) | 
| PFI 9 | P0.25 (pin 3) | 
| EXTSTRB | P0.26 (pin 45) | 
| AI HOLD / SCANCLK | P0.27(pin 46) | 
| CTR 0 OUT | P0.28 (pin 2) | 
| CTR 1 OUT | P0.29 (pin 40) | 
| F OUT / FRQ OUT | P0.30 (pin 1) | 
Keep in  mind that not all outputs are available when using the BNC-2110 with M Series Devices. Only 46 of the 48 DIO pins are accessible. 
Also if both connector blocks are used and a counter is required, you must connect to ctr0 on BNC Connector Block 1 using PFI 12 from the M Series Device. The counter output on Connector Block 2 is a digital I/O pin (pin 0.28) and not a counter. ctr1 is a digital I/O pin on Counter Block 1 and on Counter Block 2. 
Signals are verified in reference to any digital ground pin on the BNC-2110.