Could it be that your collimator opening, source and scatterer are not in line? Could help to check the alignment, since you use a quite tiny collimator opening.

Yeah, I agree. So I decide to try some different diameter of collimator. But if it is too large, it is dangerous (since I use 5mCi 137Cs), and if it is too small, the coincidence events are rare.

5 mCi of Cs-137 is not such a dangerous source. You will have a dose rate of roughly 14 micro Sv/h at 1 m, if you have a direct line of site, so nothing really dangerous. Normally for such experiments we used collimators with 5 mm opening and a 10 mCi source. Of course, the student has to be taught not to stay in from of the collimator or you can place the whole experimental setup behind some supplementary shielding.

Dosimetry concerns. Obtain a dose meter and measure the dose rates for the local background, leakage at the surface of the source holder, and for the primary beam.  Compare measured dose rates against limits for public exposure (hint 1 mSv over 365 days) and for radiation workers (hint 20 mSv averaged over 5 working years, each is 50 weeks times 5 days of 8 hours). The primary beam should be directed towards a suitable beam stop.

To check the geometry, consider the single event rate recorded by each detector. Try to increase this by adjusting one geometrical parameter at a time (distance, collimation, x/y allignment etc). A large collimator increases the event rate at  the cost of degraded energy resolution,

Coincidence detection allows the MCA to measure the energy of the recoil electron. The coincidence rate is small fraction of the singles rates, so ensure these are as large as possible. In addition, the experiment requires the delay line NIM module, and this be adjusted so that the pulses reach the MCA at the same time. Remember that a delay of zero, removes the true coincidence events leaving only the randoms. Use a dual channel oscilloscope to monitor both pulses, check their polarity, amplitude and timing characteristics. Be systematic and check each step of the counting chain for both channels.

Read the manual for your MCA to understand how it can be used for gating or coincidence detection.

Lastly, true coincidence detection rates are small, requiring a few minutes or longer to gather enough data to separate the signal from the background noise of random coincidences.

Good luck.