Keiryu line holders are even more important than tenkara line holders. I keep lots of tenkara lines just coiled up and slid in 3" x 4" ziploc bags with slips of paper noting the line weight and length. That works fine for size 3 or 4 tenkara line. Try that with size .8 or .4 keiryu line and you would have a tangled mess, which like a Gordian Knot, can be undone only by cutting it to pieces.
You could just use a couple of the Small Tenkara Line Holders. However, if you make your own lines, (which is what keiryu anglers do instead of tying flies) you will probably soon want more lines and a more compact method for storing them.
Luckily, several solutions to keiryu line storage exist.
The nicest system by far is one like the Daiwa Tankei 1500SK, which is a waterproof case holding ten individual line winders. Do you really need ten? You will use at least a couple for tenjo lines, the slightly thicker, possibly hi-vis upper portion of the keiryu line system. You will use more for the lower portion of the lines, as that is where you will have the variation in line length and weight.
But ten? Well, if you have a Suntech Field Master for example, the rod can be fished at three different lengths. The rod is rated for lines of 5X, 6X or 7X. That's 9 possible length/weight combinations right there. However, even if you only fished with 5X line, if you made two lines for each length, that would take six winders. Add two or three tenjo lines and you've used 8 or 9 winders. Ten is not too many.
You will definitely want to make up spare lines at home. Rigging keiryu lines streamside is about like tying flies streamside. You can certainly do it but it takes quite a bit of time that could be more productively spent fishing. And if you do rig a line streamside, you will need a line holder to wind it on anyway or it will be a tangled mess the next time you go fishing.
Size 5.75" x 2" x 1"Daiwa Tankei 1500SK - $39
The Owner bamboo line winders are positively low tech by comparison, but they do get the job done. They are sold for tanago fishing but you can easily hook the hook on one of the two metal bars and wrap your line around the bamboo cross pieces. The ends of the long pieces have slits to hold the end of your line.
The biggest disadvantage is how to store them. The Tanago Tackle Box will hold three or four, I believe, which would be the absolute minimum you'll need - one or two for tenjo lines and two for lower lines. More would be better. (And don't put them away wet. The bamboo can get mold.)
The Tanago Tackle Box will do double duty as a keiryu tackle box, holding two different sizes of hooks and three sizes of split shot (or three sizes of hooks and two of split shot), plus three or four bamboo line winders or even more of the foam line winders. It will fit in your pocket or in a ZimmerBuilt Strap Pack.