It can absolutely be done.
Aliens, space travel, lasers, new weekly sci-fi concepts. This is the core of Green Lantern, and has been done over and over and over on TV for years.
The problem, and by my account the only significant problem is... 'how do all the constructs on a TV budget' and the answer is simple: you don't. In order to do Green Lanterns on TV, the powers of the average Green Lantern would have to be reduced to that of your average TV spaceship: shoot lasers, block with forcefields, fly through space. That's what an average GL does, so make that canon, that that's what an average GL does.
Now you still do constructs, but make them something very special that only gifted/chosen/extra talented Green Lanterns can do. Your Sinestros, your Hals, your Johns. And even then only with great willpower and ring charge usage. And then make them practical effects, more of an object summoning power than anything else. If GL is going to make a sword, have the prop guys rig up a green sword. If he's going to make a giant baseball bat... make it. If he's going to make a green suit of battle armor... well... clearly it's the season finale. You can even do Hal's trademark hand/glove/punch stuff actually by superimposing a hand and doing the results practically, though there's a bit of cheese there, it's a cheesy move even in the original comics. So, that really is the key to doing a GL show on TV: maximizing practicality, something the comic never had to take into consideration.
The hardest power to deal with would actually be flight, as you'd basically have to string people up in harnesses on green screen for hours in order to shoot the space fights and space travel conversations. After that, superimposing them onto space (no need for shadows or other integrations) with a green glow is incredibly easy, as SFX shots go. The challenge would be atmospheric flight, where you'd basically have the GLs doing up up and away in the Lois and Clark Adventures style as opposed to GLs leisurely floating in the air.
In further interest of practicality,
all the aliens become rubberforehead aliens. You'd need an experienced prosthetics team, perhaps even culled from sci-fi TV veterans but Kilowog isn't a tougher nut than, say, Star Trek's
Morn. Salaak does not demand more CGI than Dr. Who's
Moxx of Balhoun. Even the Guardians need not appear more frequently or more alien than Stargate's
Thor. All these shows have smaller budgets than Arrow or Flash, by all accounts. It's not about having a big enough budget to do aliens.
Other than the powers being nerfed, the major tradeoff would be a need for 'bottle shows' either with GL grounded on Earth, either without charge or without mission to deal with Ferris Aircraft and the Earth cast or on some practical standing Oa sets for basic training, day to day GL procedures or some other CGI-less thing that a more personal story can be sat upon.
So there are definite limitations on a TV budget, but the core of who Green Lantern is, the coolness of our hero creating something out of thin air, and the functional action of his stories are all very much doable (and have been done) on a TV show. Patrolling alien planets and facing utterly unique problems, dealing with a corps of aliens with a creed and internal politics, using incredible sci-fi devices creatively to solve said unique problems. To me, that makes it worth it, that makes it possible to do justice to the character, even if you can't do all the spectacle of a movie. I believe these characters are awesome enough that they're still compelling without major spectacle, just like your Dr. Whos, your Jean Luc Picards, your Mal Reynodses.
I would dare say that limiting GL's powers in this way makes him a more interesting character for drama and tension and resourcefulness. I can recall the only times I liked Hal Jordan were when he was low on charge and had to use his limited charge well while at the same time finding a creative way to get a recharge, or not. If that happened every week, even Hal-averse guys like me would love the character.
Long story short: Nerf the powers, do a Dr.Who/Star Trek mashup type thing (with a higher budget!). Rake in the success.