First off, you seem to be looking the Greenville, NC area and not Greenville, TX. You should see a tab at the top of your Trulia page that says "Rent". I'm about to speak Trulia heresey but there are other web sites that list rental properties.
You can call any REALTOR in your area. They will show you any home. They have access to the MLS and can enter your search criteria and have the homes that match you emailed directly to your inbox. You will be able to scan through the pictures etc, make a list of the homes you like, then tell that same REALTOR which houses you want to see. The REALTOR will sched the appts for you. I am a REALTOR & do not charge my renters to find them a home. The owner is the one that pays the REALTORs fee. http://www.txrealtyforyou.com/
Hello. You are in Greenville, Texas, correct? There are several rental companies here in Greenville. You should try talking with one of them. There is Huntex Properties, Mary K Properties, Tarpley Realtor, Mid-town Realtor, and maybe one or two more. I know the best way to find a rental house is to drive around the area you like best, write down numbers and street address and call people, or look online.
Marsha Bane of Bane Properties has several houses for rent. She is probably the nicest woman you'll ever meet. It is worth the call. 210-651-9659. Leave a msg and she WILL get back to you. Martha Valiquette, REALTOR.
I would put you in contact with an agent that I work with that also is a Property Manager. I also know several other private individuals that have rentals. I will only send you to the ones that I have a relationship with and know that they will treat you well.