Craigslist is the absolute best place to search for a rental home. As a landlord, I don't even post elsewhere, as that is where all the serious renters search. You can also try Oregonlive.com and may find property managers list properties there. Trulia of course has a rental section, but I have personally never even looked at it. Also, many rental companies have large inventories of homes, so if you inquire about one of their properties, ask for a list of all homes coming available. Most landlords probably don't realize that pigs can make great house pets, so you may want to provide references from past landlords, or perhaps a few letters from people that know your pig and can attest to his awesomeness.
If you have a specific neighborhood in mind, cruising the streets for rent signs can't hurt.
Also, there are very few one bedroom homes- if you are trying to save money but still want something that feels like your own, you are more likely to find one side of a duplex.