My dad used to take me out to dinner.  He was trying to teach me how to behave at a fancy dinner or dinner party.  I think after age 10 I never spent any one on one time with him.  I think it is great you are trying to do this!  Something as simple as an outing for ice cream- ya know- monday take one kid, tuesday another.  Something like that.

Take one on errands like to Home Depot the drug store etc. Kids want to be with you every encounter does not need to be an event.

Play with one in the yard for 30 minutes or so. Are the little ones napping and the 6 year old up? Play a game, hide and seek, candyland toss a ball…

One dad I knew took a kid to breakfast every Saturday. Sometimes they had deep conversations sometimes not.

Are you grilling? Take one outside to hold the hot dogs. Mowing the lawn? Get outside to hold the bag or whatever.

Read one a story at night. The other three with your wife. Bathe one.
You can do it.

When I was a child (more teenage years), my dad used to wash the dishes and I would dry them and it was nice to have that time together.

My Dad did the one on one thing with me too and I have to say it felt artificial to go out to dinner together. This was when I was around 10. I longed for him to just be with all of us (my sibs and my mom more). And what bonded my sibs and my mom and I were the more mundane things—like the dishwashing mentioned above. One caveat—I did enjoy really special outings which were maybe once a year when he took me to the ballet all by myself.
I heard good advice in another thread (and here) about including him on errands—taking the car in for an oil change? Take him along, you can chat in the car, maybe read a book you brought as you wait, or point out the colors of the cars and stuff.
The other good advice I heard was more for an older sib feeling left out which is not your case but may be good here—have him help you with the younger ones in a way that makes him feel special. So say you are filling up the kiddie pool with water, he can help because he is old enough and the others can watch. You don’t want to create rivalry so of course you can have them “pretend help” by putting some water in a small bucket they can handle so they all feel like they helped but the older feels special too.
I think it’s wonderful he is asking! To be so in touch with his feelings and can express them shows you are doing something right.

I agree with babydreams.  I think it’s fantastic he is asking, and verbalizing his need to spend time with you.  I also thing that it’s fantastic that you’re listening AND sourcing out information to make it real quality time for him. 

I’m forty, but memories of spending one on one time with my Dad from my childhood, still generate the same feelings the experience did.  Like the others said, it doesn’t have to be an event every time.  I had a mix of things with my Dad.  We were from a small town, so it wasn’t like he could take me to the mall or even a movie.  But my one event would be random breakfasts out with just him and I.  I LOVED those Saturdays. 

Being where we were from, non-events were more our thing.  Chores like the others mentioned, were another alone time for us.  I particularly liked when we would go out for the day to cut wood to bring home for the woodstove.  Sounds mundane, but I think it was just about the two of us going off in the truck together, working for the day, and then getting home and unloading it all.  The praise and appreciation I recieved from him and my Mom for helping out was probably a big part of it too.

And errands were already mentioned, but I enjoyed grocery shopping and going to the hardware store, especially when Dad asked my opinion about choices to be made regarding purchases.  I felt like I was important and I was doing more than just tagging along in order to stay out of Mom’s hair. 

Last but not least, when I was older, I would go home with Dad from school, rather than take the bus.  I would walk to his work and wait for him in the truck.  It didn’t get me home any earlier, and the drive home was only about 7 minutes, but I just enjoyed discussing our days and having that one on one time after being apart all day. 

Anytime spent going anywhere with my Dad in the truck as opposed to the family travelling in the car was special.  Sometimes we didn’t even talk much until we got where we were going, but it was just the feeling of it being just the two of us.  What we were doing, where we were going, or what we talked about didn’t really matter.  It was just knowing that my Dad wanted to spend time with me as much as I did with him.

One last thing to add, and that would be do unexpected things.  Like if there’s going to be a meteor shower that’s visible that night, wake him up to see it with you.  Leave school and work early one afternoon, just to go see a movie.  Or take an extended lunch hour together. Missing a little bit of school once in a blue moon won’t hurt, and will make even the most boring brown bag lunches special. If you’re home alone together, have dessert for dinner.  One bad meal isn’t the end of the world, and it will make quite an impression.  The unexpected element to things, will really make lasting memories, that I’m sure he’ll still remember fondly when he’s forty. 

My son is an early riser, and sometimes my husband will take him for a walk or swimming early in the morning, and let me sleep in with our daughter.  My son loves hanging out with just his dad.  At bedtime, one of us does his bath and bedtime ritual while the other is with the baby.  It really doesn’t have to be anything big, it is about the child and parent having one-on-one time.