Have you made your lawn nice and clean?
Does the paint on your house look good?
Is the interior warm and inviting?
Could potential buyers walk in and easily imagine moving right in?
Is your home priced right for your area?
Is your home being advertised to attract all the willing and able buyers?
These atre the things that will sell your home. Potential buyers will understand that cars have to park on the street.
From what you said, your neighbors are parking their cars outside of your house legally; then the only way to approach them is to ask them nicely and see if they can help you because you are selling your house.
I don't know about your relationship with your neighbor; hopefully, it is decent. They should be very happy to help, especially since the market is slower, and they should care about preserving the neighborhood property value.
Perhaps you can bring a little present over, such as a bottle of wine or what not, and see if they don't mind helping; especially around broker open or other open house dates as well as when buyers might come and inspect the property.
If you don't have a great relationship with them, perhaps you can ask your Realtor to help you out. Hopefully you have found a Realtor who is good at building relationship, he/she can help you that way.
Like everything else, a little politeness and respect go a long way when ask people to help you.