The problem you are likely to have is in attaching to something solid. When someone grabs a stair rail it must hold them from falling in any direction. Factoring in the leverage they have from a rail 36 inches above the surface and you have a tremendous lever arm and a lot of force at the attachment point.

Wooden posts need to be relatively large (3x3 net) to work as supports for a handrail, and need to go into the ground at least half the height above the ground or be fastened solidly to masonry using expansion anchors. The anchors need to be spread out enough to create a solid attachment. 6-8 inches apart is typical.

Other methods include driving 2 inch angle iron into the ground and then bolting the wood to the angle iron (through fasteners, not lag screws).

Steel may also be mounted in holes in the masonry and the post bored to match. The metal would be at least ¾ inch square tubing (just like a metal post). I would consider using about 1 inch diameter round steel rod mounted into bored holes in the stone and substrate (you need at least 6-8 inches) and then a mating hole in the bottom of the post for at least 10-12 inches deep.

The picture you have does not comply with modern codes since there are too many steps to not have a handrail (though local interpretation and codes may allow this setup for exterior landscaping steps).
If it is actually entering a house you will need to comply with the code (no landscaping escape).

I know this is an old message but I've arrived to this forum now that my kitchen is done and am starting on the back yard! I have a similiar situation- we are replacing our concrete landing/steps off the kitchen with a limestone capped stone landing. The height will be about 21 inches (3 stairs high) and both my contractor and husband do not think it needs handrails. I do, as we will be putting a cafe table and chairs on it (it will be 8x10 feet) and I worry about kids falling over the edge! Are there any solutions besides an iron railing? Any pictures of the previous suggestions?

Thanks!

Check with your AHJ but outside steps only 3 high often are not required to have a handrail.
It is also getting harder to have wood railings meet the code rules for size and grasping if a rail is required.

Thanks! I will check but also thought I might have the stairs built and see if I think they need a rail. I'm asumming a rail can be put in after they are built- am I correct?

Thanks for your help.