There are some great NI-DAQmx triggering examples that install into LabVIEW 7.0 or newer when NI-DAQ is installed (as long as you include support for your LabVIEW version when installing NI-DAQ). With the release of NI-DAQ 7.4, both of your devices are supported by NI-DAQmx, so I would definately recommend using the DAQmx API. In LabVIEW, go to Help>>Find Examples. For your analog board (6110), navigate to Hardware Input and Output>>DAQmx>>Analog Measurements and maybe take a look at Acq&Graph Voltage-Int Clk-Dig Start.vi. For your digital I/O board (6534), go to Hardware Input and Ouput>>DAQmx>>Digital Measurements and try Read Dig Chan-Int Clk-Dig Ref.vi. Both of those examples has a control on the front panel that allows the user to select whether he/she wants to trigger on the rising or falling edge of a digital signal. Hope this helps!
-Alan A.