It depends greatly on his furnishings. Do you have a photo of the room in question? I can understand him being perfectly happy with it. It feels like home to him. If you don't have photos my guess would be a nice soft off white though.
Oh and when you're over there, give him an extra hug from me. I can no longer do so with my own Daddy and it helps when I know others give their Daddy's hugs from me.

Hi, Catkin,
I just had the same dilemma in my mother's LV/DR. The carpet is 40+ years old, but she is so proud of it, because it is pure wool and not worn out! It is pretty bad, but she will not change it.
Anyway, I just repainted and I am sorry I don't know the color. It was a Sears Easy Living paint. On the color chart for the whites/neutrals ----- it is a tri-fold and in the center section, it is on the far left, I think the second one down. I can see the color chart in front of me, but can't remember the name - and threw out the can.
It has a bit of gold, a bit of brown and reads a very soft neutral on the walls.
You just want to be careful of the yellows, golds. No matter the furnishings, the walls will pick up that avocado green color. The last time I painted the rooms, it was a bit too yellow.

My dad was much the same way! I like the idea of a creamy color, perhaps going in the yellowy color of the inside of an avocado (at least you know the colors would go well together!). I think white or off-white might look a bit stark and maybe slightly dirty against the avocado.

There are some light khakis that have a greenish undertone rather than a pinkish undertone.

Last weekend I was in a large flooring retailer in my area and there was a whole rack of sculpted carpet--the big sample was avocado in color:), and it was among their high quality lines.

I had that color carpet in my apartment in the late 1970's. It was shag, too. I didn't even like it then. But I found it surprisingly neutral. I had goldish draps, beige chairs, and a blue sofa and everything looked fine together.

It is a shag! A short shag ;)
I really don't want to go the yellow route if I can help it.
I wonder about an off white, and I wonder why we can't just look at the fan deck, pick a color and go with it!!!!! LOL

For a while I rented a condo unit that had similar carpet throughout (and matching green tile in the bathrooms).

If a large element that you can't change isn't to your taste, the key is to avoid both playing to it and playing against it. Specifically, do not use a wall color that is a direct or near complement complement of green: that is, not red (or pink) and preferably not orange or purple, either, because all of those will make the green stand out instead of recede.

I have deliberately used green carpet with pale yellow walls, but it was a grass green, not avocado. In this case, I would prefer a greenish khaki (not taupe - too pink!) or beige, which will somewhat blend with it. And not too light; the color has to be strong enough to withstand the green light that the floor will reflect.

BTW, if the element that you can't change is a pattern rather than a solid, using more of the color that stands out too much is a way to tone it down. The same rented condo had bathroom cabinets clad in laminate in a violent gold pattern (this was against the expanse of avocado green tile), and I found that using a gold shower curtain and towels calmed it, because it made gold a background color rather than the foreground.

Thanks for weighing in!

I've decided on SW Alabaster (in a similar Behr color).