killing bermuda grass and starting a new lawn

I live in Santa Cruz, CA, and have a very small (about 20 by 12 feet) back yard chuck full of bunch and bermuda grass.  Is there an organic way of getting rid of this grass and putting a "nice" (not bermuda or tall rank bunch grass but soft green grass) lawn?  I know about using black plastic or clear plastic but that's not practical for me because I use the yard every day and don't want to look at and walk on plastic for 6 months.  I don't think I have the energy to remove it all by hand either.  Thanks for any suggestions. 

I usually think in terms of one plant outcompeting another.  In the farming world, this is referred to as "smother crop". 

For this summer, you might check out groworganic.com and order buckwheat.  Buckwheat will grow to three feet tall very fast and cut off all the sun going to the stuff below. 

Another would be cowpeas - it doesn't grow as fast, but it fertilizes your lawn at the end.

In your case, I would think that buckwheat would be a better bet because you are growing warm season grasses (which I don't know much about) and you would need to plant the seeds in the summer.