I've received some pictures of great looking troughs made with leaf and grass clippings and pine needles.
The maker runs the material over and over with his lawn mower until it is fairly fine. Then spreads it in the sun until all the green is gone then uses it just like peat.

Go to a garden centre and get compressed blocks of coir,a cocanut byproduct.When exposed to water,the blocks swell up to many times their original size.Others have used this stuff with some success.And,I agree about peat.It IS anon-renewable resource.But,I'm as guilty as others here;I use peat,although when I run out(I don't use it much except where weight is an issue)my wife will have me use coir,something she uses in the garden.
Cheers from here

You can use vermiculite or perlite in place of peat moss.

As far as that goes, why wouldn't compost work? I have composted leaves, sawdust, grass clippings, etc. After a year, it looks just like peat moss. Very fine texture. Why wouldn't that work??? As long as it is sifted, and is very well composted????

Compost might be a problem in that some of it might be too fine and not allow the tufa to cure.

Peat is "mined", right? So is Portland cement and vermiculite. If I understand mined products, none are renewable. "Creating with Concrete" by Sherri Warner Hunter says plain potting soil, without fertilizers, can be substituted for peat moss. I've been wondering about using shredded newspaper.

"In 1999, 1.2 million metric tonnes or about 10 million cubic metres of peat were produced in Canada. This volume of peat harvested each year is small in comparison to the estimated 70 million tonnes or more of peat that accumulates naturally each year in Canada. "

I don't think we have to worry about peat running out any time soon.:)

Here is a post on paper crete, might be helpful. I haven't worked with paper much, but the little I've tried has been out in the rain is still in tact. You eliminate the soaking part of tufa also.
bonnie

Here is a link that might be useful: paper crete

David,we may not run out,as you say,but we're,by using it,contributing to the slow destruction of wetlands,unless you know where your product comes from.We may not have problems here(yet) but in other countries,the resource is in decline.My wife is a Master Gardener(a title which many who work the soil in the Northwest know)and was counselled in her classes that it was not good to continue to harvest peat moss.I don't disagree with the use here,I'd be in the minority to do so.But,remember that our forefathers said"There's so many of them,so why worry?We'll never be able to kill ALL the passenger pigeons...".As the original question was asked,what other products can be used,that's been answered by several people.And,there are viable alternatives.Let's all of us try something not peat in the near future.
Hmm,we get a lot of dogs here.Do you suppose...?
Cheers from here

Kim, you are right, Portland cement, perlite and vermiculite are made from minerals. All these are inorganic materials, " mined". If you want the "tufa" look, you have to use some organic material mixed in the cement. With time organic materials break down, creating the porous texture.

Papercrete!Thank you,Louisiana greetings,this seems my kind of thing--and I can use up my junk mail,whoopee!