For an example, I created General's Outpost, Observer's Outpost, Assassin's Outpost, Archer's Outpost, and Shaman's Outpost.

Added Heart of the Soil, Mind of the Spray, Claws of the Brush, Sweep of the Overhang and Lungs of the Canopy. I really wanted to figure out a way to remove the mana ability from a land altogether, in a way that 'all lands must have a mana ability purists' would at least begrudgingly accept. Came up with a few, but nothing to bank a cycle on. So, you know, sliver-ish man lands. I suppose we could just do those.

Oh, nice challenge.

My head may be too absorbed in the last challenge, but it occurs to me this would be a good time for a non-colour cycle of colourless-producing lands, like a cycle of Haunted Fengraf for different card types. But I can't think of anything I'd actually be excited to print.

My entry for the previous challenge was a cycle of lands too... so I wanted more guidance/restrictions. So I rolled d110 to find another challenge to combine with this one. After a couple that didn't work I rolled Challenge # 033, which I interpreted as telling me to create a cycle of five lands, each one related to one of the last 5 cards created for that challenge.

So I created Caldera of Offering, School of Alertness, Amphitheatre of Duels, Grove of Might, and Graveyard of Unrest.

­Sundrenched Valley, Windy Chimney, Flourishing Thicket, Firey Canyon and Consuming Mire, a cycle of lands with discard effects.

I liked this challenge a lot, but I was too busy to think of a cycle I liked. I'm not sure activated abilities from hand quite count, but they're technically within the terms of the challenge.

­Living River One entry in a cycle of man-lands with always-on static abilities. I haven't finished the cycle.

Link created cards Crystalline Ashlars, Lore-Riddled Cliffs, Nightmare Realm, Volcanic Roost, Volcanic Roost with a static ability affecting a different creature types.

­Narrow Clearings, one element in an as-yet-unmade "terrain" cycle, but with no new rules baggage, seeing if I can make terrains as subtypes of lands after all, with static abilities.

Thanks, Jack. I hadn't made it back to my computer to link to those here. You missed Woven Canopy.
The best example I can think of for a static ability on a land is Reliquary Tower.

Yes, I kept thinking of reliquary tower, but I couldn't think of for more :) I considered "opponents can't look at your hand" but that had rules problems and was very narrow. And then I got stuck. The "minor tribal benefit" was a good idea.

­Conquered Treeline, a triggered fetchland ability.

I am trying to think of a cycle of lands that turn into auras, since the difficulty of putting abilities on lands is that it represents a significant card advantage to have an effect with a card you may already have in your deck, which is neatly offset by the disadvantage of auras that they usually represent card disadvantage.

I like the idea, but unfortunately, I can't get the text to fit on a card! Auras are so wordy. By the time I've got "Becomes an Aura Enchantment with Enchant Creature, attach it to target creature" and "ETBs tapped", there's not enough room for an actual effect, even assuming I save room by giving them basic land types which go away (without reminder text??) when they turn into auras, and ignore whether they're tapped at the time.

I've tried several variants. Making a keyword and having all the baggage be abbreviated as reminder text (which still isn't quite good enough). Making them be "Enchantment Land -- Forest Aura"s which has all sorts of rules problems and doesn't help that much. Having them have an alternative casting cost, rather than going land->aura in the battlefield.

I also considered having them give a bonus to a creature without attaching to it, but that didn't have the nice matchup of card advantage/disadvantage, so would have to costed quite expensively, like equipment but more so.

The only thing that seemed plausible was "3GG: Exile this under target creature. That creature gets +3/+3 and has trample." That just fits, but cheats by putting the card in exile away from all removal spells. Either land destruction or enchantment destruction should work on it, preferably both.

Can anyone think of a way which would work better? Or should I accept this isn't going to work?

I would use DFCs.

­Urborg, Tomb of Yawgmoth has a static ability. So do the Adventurers' Guildhouse cycle and The Tabernacle At Pendrell Vale, but those may not be very good examples to follow ;3

Jack's idea reminds me of the plan I had for Sienira's Facets, a card with type "Artifact Land - Plains Equipment". In the end I rejected it because the flavour was just too weird.

I don't have a good suggestion for any way to make it work. Apart from DFCs, as Link says, which do let you bypass the complication quite niftily. And it's even a take on DFCs that I don't think is included in Mirroria, which just goes to demonstrate how insanely large the design space of DFCs is.

I did think a lot about Urborg, Tomb of Yawgmoth. It was an elegant way of having a static ability on lands that felt like it BELONGED on a land, not just a spell-like effect tacked on. But I couldn't find much more design space along those lines, at least, not at common :)

Ah yes, having lands with an "equip" works well, if they ETB as lands, but still have a mana cost to be equipped. Although presumably need to say "you can't tap this while it's attached". But yes, works a bit less well flavour-wise.