I got a $40 parking ticket on a Sunday in Los Angeles on a car rental.
 You were allowed to park on the street I was on, every day but Sunday
and I had thought Sunday was OK- however in looking at the street
sign, after getting the ticket, I realized it wasn't.  Is there any
way to beat a parking ticket for a car rental when you live in the
same state (CA) as where you rented the car and got the ticket?  The
car rental was offered by my insurance coverage when my regular car
was rear ended and being repaired. Would the insurance coverage cover
the ticket?  Is there any good way of dealing with this to avoid the
$40? Thanks.

I would say that sence it was you who parked there, you should pay the
ticket. As far as traffic tickets go, this is not that bad. I assume
that you feel the ticket should revert to the owner of the car (the
rental company). If you had bowered a friend's car, the ticket would
eventualy fall on your friend because his/her name and address is tied
to the licence that the officer wrote down. However your friend would
be well within his/hes rights to demand restitution from you, although
it would be hard to prove in court.

This is all moot because the contract you singed with the rental
company would most definatly contain a provision stating that the
renter will bare the costs of violating the law while using the
vehical.

If the ticket is not paid in a rather short period (e.eg. < 7 days)
the ticket with will be processed by the municipality and the car
rental company will be billed.  The moment that rental agency gets
notified they in turn will simply lookup whoever signed the rental
agreement.   If that is you, then they will automatically bill the
credit card for $40 PLUS an admin fee and mail you the transaction 
record.  Alternatively, on the slim chance the rental agency had the 
agreement directly XYZ Insurance, they will just add it to the total
owed for your courtesy car (along with surcharges like fuel-not-full,
excessive dirt, scratches and scrapes).

Nobody likes parking tickets, but that's the way it is.