How to ask for cash in wedding invitations without appearing rude can be tricky. The first thing to say is, don't! Some of your guests will find it rude. Saying that most of your guests will ask for a wedding list so you will need to ask the help of your parents and close friends and family to pass on the request for cash. Your guests will understand that having cash is much more useful to help you start your married life.
Most people will include with their invite a wedding list card or a little note about presents. A simple note saying that you are saving up for something would work, I don't think you need to have a cute poem to ask for money. Ask your parents or older relatives their views on how to ask for cash in wedding invitations as it is more likely the older guests you will need to win over!
If you are planning on creating a wedding website then you could have a note explaining that you would love money to help you for your new home together.
Having a honeymoon fund is another way for guests to help, take a look at my article on how to set up your honeymoon registry.
Older guests may want to buy you something from your wedding list and to please them you can have a small wedding list at one of the local stores, there will always be something you need for the house.
For those guests that do want to buy something you could set up a sofa (or another large item) fund as my sister and brother in law did. Some also have collections for the deposit on a house.