Good LEDs run about $1000 each. Cheap LEDs won't do the job.
Options
1. Use conventionals, bought used with dimmers if needed https://www.usedlighting.com/27174/altman-3-cell-cyc
2. Rent
3. Buy cheap stuff and live with the results- dim, uneven coverage with limited color range
I have had luck with using two colorblasts to crosslight a similarily sized (bigger, actually) cyc. that's a solution for around $1k. At that budget I don't think you're gonna get a nice traditionally lit cyc if you go with LED.
It is probably past the point, as this was posted in Jan, but lately on low budget shows, I rent 6-8 LED Pars and put them on booms SL and SR and wash a small cyc that way. You can try for LED Strips from Clay Paky or Philips and get results to, but it will they aren't as widely found in all rental houses. Good Luck.