How big are your plants? How many have you got? What is your space?
I had a few ideas come to mind, but none really work in all circumstances...

The easiest would probably be to find a flat that has compartments, like a self watering tray or an egg carton. (Not working with solo cups here, so I don't have an exact grasp of the size), anyways, find or build something that holds them in place...
Myself, I put mine in a ceramic or glass outer container - old coffee mugs and the like, that keeps things bottom heavy.
Or you could add a few rocks or marbles before adding your potting medium.

Great suggestions!
I put mine in all sorts of slightly larger and/or taller outer containers, like sleeves, to weight them down and support leaves. I am not working with solo cups, so I don't have a specific suggestion. I often use slightly larger, sturdier plastic pots, such as 3" Perhaps those who use solo's can advise better. (Almost all of my plants in various size pots are in double containers for that reason. Otherwise, I seem to always be tipping them over and spilling the potting medium all over the place. I have to remove them from the outer container to water.)
Joanne

Cork,

Put your solo cups into clay pots. You can find them at Michael's and they're not expensive. Easy-peasy.

Linda

This post was edited by whitelacey on Sun, Dec 15, 13 at 4:09

Linda -

I was expecting a lecture on it is not DIRT - it is soil - soil becomes dirt when it gets under your nails.

Cork - I agree with you 100%. Before they sold small black polyethylen square pots- but they are gone..they were sturdy - you just needed to make a label for each one instead of writing with a marker on a solo cup.
What I do - when I am working with solo cups and cuttings - I put wet felt on the bottom of the black tray - get a dome - and keep stacking them tightly until the tray is filled - ad only then move it to the shelf - less tipping of the pots. If I use the solos for the semis and minis - I move them to the shelves one by one, not on a tray.

I.

I was trying to be nice... ;)

Linda

I use trays with a high rim to house my plantlets. They can only rest against the wall of the tray when tilted.

Where do you get these trays?

Kitty litter trays?

Get these from China. Made from Polypropylene for general storage purpose.