As a monogreen player the trick for me to construct viable decks is to, as Zherbus points out, ignore many threats. How do I try and accomplish this? By having sufficient speed in my decks, which essentially boils down to fast mana and fast creatures. I have on occasion built slow green decks that rely on combos to lock down my opponent. Below are two examples of my decks ideas... I have to be innovative because I am a monogreen player... and especially since I don't believe in using other people's decks.

Monogreen beatdown/aggro (I may not use the correct term for the deck but this is how I refer to it)

15 Forest
1 Mox Emerald
4 Birds of Paradise
4 Llanowar Elves
4 Elvish Spirit Guide

4 Giant Growth
4 Rancor
4 Berserk

4 Greater Good

4 Yavimaya Ants
4 Branchsnap Lorian
4 Viridian Zealot
4 Pouncing Jaguar

This deck has succeded more than I originally had expected, mainly because of Greater Good. Without it the deck would stall after 5-6 rounds of play but after I introduced GG some funny and insane card drawing makes it continue until the opponent dies. The most difficult opponents so far are other creature heavy decks. Against recognized good decks, I've only played Hulk Smash (6-3), Sui (9-3) and Fish (5-4).

Monogreen rogue/control (same as before, this is how I refer to the deck)

14 Forest   
1 Mox Emerald
1 Sol Ring
4 Llanowar Elves
4 Fyndhorn Elves
4 Elvish Spirit Guide

4 Root Maze
4 Winter Orb
2 Null Rod
4 Tangle Wire
2 Damping Matrix

3 Wasteland
1 Strip Mine
4 Viridian Zealot
4 Yavimaya Elder

4 Troll Ascetic

A strange deck that surpringsingly works best against decks that use few creatures.

These two decks I posted to illustrate the point that some people have made that it's viable, at least for a while, to play with innovative decks (or unusual as deck #1 is a no brainer).

I also have a monogreen Hurricane kill deck which is completely creatureless. It utilizes the Ashnod's Altar + Fecundity + Saproling Cluster and Zuran Orb + Fastbond and kills with Hurricane. It's not very viable  but it's funny to get the combo going and win with a gigantic Hurricane.

It looks something like this:

21 Forest   
1 Mox Emerald
1 Sol Ring

4 Fecundity
4 Saproling Cluster
4 Ashnod’s Altar
2 Thran Foundry

3 Naturalize
2 Eladamri’s Vineyard
2 Zuran Orb
4 Moment’s Peace
4 Nature’s Lore
3 Isochron Scepter
1 Fastbond

4 Hurricane

Anyway that's all for me for now