Vikas Anthati (http://qr.ae/TUNGSV) referred to me to https://www.sabrentkaro.com, where one can rent monitors: https://www.sabrentkaro.com/search?st=monitor+&loc=hyderabad
For example: https://www.sabrentkaro.com/rental/rent/786 (mirror)
They seem to have some pretty bad online reviews though (Google Reviews, Facebook), but it worked fine for me.
The website asks for a PAN number: you can put a random (but valid) one. The website asks for an Indian phone number to be able receive some OTP to register on their website: somehow the website has some bug and I managed to go through it without having using any Indian phone number (you'll need one though when ordering the monitors so that they can call you when they'll get lost trying to deliver the monitors).
When renting through sabrentkaro.com, the actual provider who came to my place to deliver the monitor seemed to have their own business:
https://www.rentsher.com also rents IT and AV equipment but currently doesn't have any monitor (only laptop, TV, sound speakers or even LED Display Van).