I need to transfer the deed/title on my rental property in San Diego to my dad. Can this be done in a manner that avoids a taxable event?

It is unlikely to be a taxable event as the transfer will be treated as a gift from you to your father. You can gift up to $14,000 per year without having to report the gift. Specifically, if the value is more than $14,000, you will need to report the gift via IRS Form 709. However, it will still not be taxable to you as the lifetime gift tax exemption is $5.34 million in 2014. In addition, California does not have a gift tax.