I assume this swing moves back and forth, which probably stresses the Hardie cement board in a way that caused it to fracture. If you hang the swing again with a simple screw eye through the Hardie material you may have the same problem with the new board you install.

I think I would pre-drill a hole in the new board so that the anchor cleanly passes through the Hardie board and threads deep into the 2x4 wood above. Then caulk around the anchor shaft with matching caulk so that the hole is less visible. This would allow some flex of the anchor bolt without touching and stressing the Hardie board.

Bruce

Totally apart from the fixes to the Hardie board, I have a much greater concern that you have hung a swing in that manner. First of all, screw eyes are improper for that use (to say nothing of the flimsy gauge that was used): sooner or later they will come loose due to the repeated swinging stress on the hole they are tapped into. Second, if those are 2X4's, those are marginal for supporting a swing and will flex and possibly cause Hardie board breakage again.

If you want to do this right, relocate the swing someplace else where it can be properly secured. If you are stuck with having it where it is and don't mind the fact that you will get movement out of the 2X4's, install proper fasteners. Take a look at these videos to see various approaches to proper installation:

https://www.youtube.com/watch?v=Bl_8A1JXdME

https://www.youtube.com/watch?v=44nNfzFvmO8

https://www.youtube.com/watch?v=7jBHIpFFA3Y

The important thing to note is that these all rely on some form of bolting...not just screwing something in overhead. If you think this is overkill, you are setting yourself up for a mechanical failure at some point and someone getting injured.

Thanks, @kudzu9. I wrote 2x4 multiple times above out of habit I guess, but those are actually 2x6s. Regardless, it sounds like relocating the swing is the best move since I don't have an easy way of using bolts in my setup. I may get into my attic and see if I can access the beams closer to the edge of the roof...sounds like that would be a better way to go. I did like Bruce's idea of drilling a clean hole in the hardie and filling the gap with caulk, but the beams seem to be the way to go.

Maybe put up a treated frame and mount it on the porch itself, and have it set to mount your swing into. I would not want a swing hanging in the location you previously had it, unless those were 2x12s

scaparotta-

I knew that my answer wouldn't be what you were expecting, but I would hate to see someone get hurt. Glad you are open to my advice. Good luck.

Use a masonry diamond blade to cut it or they have so called Hardie Blade.

You can use 16 gauge finishing nails with a gun 2@16 O.C. or Siding nails by hand... make sure they Hot-dipped galvanized or Stainless Steel if you near the water.

Just get the installation book anywhere online everything is in it or get a copy where you buy your trim they usually have it.

Any thoughts on using something like these if I move the swing to the underside of the porch and attach to the joists?
https://www.amazon.com/dp/B07SKMBLMZ/ref=cm_sw_r_cp_apa_i_j8JiDb6BBVG0R

It look like an improvement, but ultimately it depend on how much load the bolt threads can support, how good you are at being sure you've got the bolts into the center of the 2X6 the swing hangs from, and whether the bolt holes get stressed over time. The more secure devices are the ones where the fasteners go sideways through the support member so that the weight of the swing and people is not pulling down directly on screw threads.