How do I get a darker engraving on stone with a 10w diode laser?

That faint ghosting is pretty normal for a 10w diode on stone. There's nothing to burn or vaporize, so all you're doing is micro-fracturing and roughening the surface, which shows up as a light grey texture change rather than a dark mark. Darker stones sometimes give a bit more contrast because the roughened spots catch light differently, but a grey pebble is close to the worst case since the mark and the base are nearly the same color. More passes won't help much, like you found, you're just polishing dust into dust. The paint fill trick does work, and it's the standard fix for exactly this situation. On a rough or porous surface the main risk is paint drying into all the little pits around the design, which looks messy. A few things help with that. Thin the paint down a fair bit so it flows into the grooves instead of sitting on top. Apply it, give it a short wait so it gets tacky but not fully dry, then wipe across the surface with a damp cloth or paper towel. The paint comes off the high spots and stays in the recesses. Acrylic works fine and cleans up with water, and oil-based paint markers are even easier since you can dab and wipe as you go. One catch: if the engraving is very shallow, the wipe can pull paint back out of the lines too. Doing a few more passes first to deepen the texture slightly gives the paint somethig to grip. Some people also wet the stone before applying paint, which slows the drying on the surface and gives you more working time for the wipe.

Another option if you want contrast without paint: drip a little clear varnish into the engraved lines and let it self-level. The wet shine reads as darker against the matte stone. That one really wants a smooth stone though, it just pools and spreads on something rough. Honestly for a garden pebble, the subtle look isn't bad either. Angle it toward a window and the shadow from the texture does a lot of the work.

I ran into the same thing on slate coasters with my little diode unit, so I feel you. The paint wipe trick was what saved mine, though mine was smoother than a garden pebble so cleanup was easier. I used cheap craft acrylic thinned with a bit of water and it settled into the lines fine. One thing I'd test first is doing the paint on a scrap corner of the stone, since my first attempt wiped off way more than I expected and I had to redo it. Also wondering if a slightly damp stone before engraving changes anything? Haven't tried that myself yet.

Rough stone cleanup got way easier for me once I stopped using paint altogether. I was doing garden rocks for plant markers and regular acrylic kept gumming up in every pit, exactly like you're worried about. What saved me was a tin of dark shoe polish, the kind that comes with the little applicator sponge. Dab it on, wait a minute, buff the surface with a rag and the high spots come clean while the grooves stay dark. Fades if the rocks live outdoors, but for something sitting on a shelf it's held up fine for me. Might be worth a test on a corner of that pebble.

One thing I'd add before you reach for the paint is to give the stone a good scrub after engraving, becasue the fine white powder sitting in the grooves actually kills whatever contrast you did get. I noticed this on a piece of slate I did last spring, where a rinse under the tap and a once-over with an old toothbrush made the mark noticeably sharper before I touched anything else. Also, are you running air assist on this? I found a gentle flow blew the debris out of the path as it cut, which let the beam hit fresh material instead of glowing dust, and that alone deepened my lines a bit.

Been messing with rocks since before I had a laser, back when we did everything with sandblasting through rubber stencils. One trick I picked up from those days that works here too: wipe the finished stone with a little mineral oil. It darkens the surface for a minute and shows you exactly how the texture reads, like when the rock is wet. Sometimes that faint mark looks plenty good oiled up. If you want it permanent, a matte sealer does something similar without the shine.