I can offer a few suggestions, however I am by no means an expert. I've had my Whites Tree Frog for less then 6 months, so just a few things I would think would come up.

So as for a screen enclosure, these can be made easily and can be bought for a relatively cheap price compared to glass or acrylic. However depending on the species you wish to house you may encounter some large issues with humidity. I own a Whites Tree Frog and I happen to have a hard time keeping his humidity anywhere higher then 50% in his Exo Terra 18" 18" 24". So I presume keeping humidity in a screen may be way harder in terms of having to not spray several times a day.

However with a plexiglass or acrylic cage you may find it's easier to keep the humidity stable.

I don't know if tree frogs can climb screen either. I will let someone else input on that as I've never seen mine climb his top screen. If they can't climb you may have a harder time with them getting on objects. However if you have lots decor that may not be a concern as they can climb that. Speaking of decor you'll have to modify your decor to attach to the screen as opposed to the suction cups for a glass cage.

If I were you I would suggest that you (should you have the materials and cash) make a screen prototype to see if it can handle the heat and humidity requirements for your species of frog. If it doesn't you can always sell it to a chameleon owner I'm sure.

If you want a safe bet I would suggest a glass or plexiglass as opposed to the screen cage. Should you go with screen I would highly suggest using a metal screen as opposed to the plastic one. As any heat will melt the plastic.

Just my 2 cents.

I'm curious what the others will say, as I've never seen a frog housed in a screen cage.

-Alyssa