You could sample the signal with your DAQ at a high rate (experiment with it), and then in Labview run the captured data signal through a low pass filter, found in the functions palette - Analyze - Waveform Conditioning - Filter (express vi). Set the filter for Low Pass, and set the cutoff frequency to 10 Hz. That will take all the ripple out and give you a DC signal. Then you can extract the data points from the signal and average them by adding and then dividing by the number of data points, or if the data points are all very similar you can use any one point as your DC value. There is also a function called Basic Averaged DC-RMS found in Analyzed - Waveform Measurements, but this is not included in the Base package for Labview. This function will give the DC component of your signal, similar to the DMM.
Another alternative is to use a hardware low pass filter (resistor and capacitor) between the signal line and the DAQ input. Then you can just capture one value, or capture several values and average them. This is pretty much what the DMM does.