Rental properties aren't as easy to locate as properties for sale. Many owners don't use a Realtor when they decide to rent their home so those homes won't be found on the MLS. Landlords often use websites like Hotpads.com, Zillow.com, Homes.com, Craigslist.com, or here on Trulia.com. Other landlords will use a leasing agency who may or may not list the property in the MLS. Some of the larger leasing agencies will keep an internal inventory.
So the point being, it takes a lot more effort to locate all rental properties available than it does to find all homes available for purchase. My advice would be to contact a Realtor who can set you up with a feed from the MLS for rental properties meeting your criteria. You'll also want to sign up for email updates on Zillow and the other sites that offer this. You'll want email updates because you'll want to be the first to know when something comes available because they go fast.
I'm sure you've heard it before but you can buy for a lot less that you can rent for in this market. Check out NerdWallet.com and play around with the mortgage rates and calculator found under the "personal finance" tab at the top. You can type in your credit score and home price to see what your monthly payment would be.
If I can help out in any way, I'm here for you anytime.
Eric Cox, Principal