If you live there you can get a resident parking permit, which allows you to park at blue spots. They're called Macaron, and you can get them at the Fondation de Parking, which is located at the 5th floor of the parking called Carrefour de l'Etoile, at the end of Rue des Acacias. 

When we lived in this area it cost about 300 Chf for a year permit. It's far from ideal; because they give out more permits than there are spots, and often you have to drive around the area for 10-15 minutes to find a spot and then park about 10 minutes away from your house. Occasionally it takes a lot longer or you're forced to park illegally (especially at night).

Unfortunately there aren't any alternatives. If you can find a box that's great, but they're hard to find at short notice and it'll cost you 300 per month. Illegal parking is not an option because they check every day.

If you don't use your car every day you could park the car somewhere else away from the center. Public transportation in and around Geneva is very good so maybe this works for you. I've never tried this, but maybe the parking at Geneve Plage (behind Eaux-Vives) is an option.

Pretty much what i thought thanks! :-/   

As for using it daily .. Parking it out of the way may be the best option i guess. Eaux-Vives is our temp accomodation, we've asked our agents to find us a place a bit out of the city, maybe towards Nyon.. I know the transport is fine in the city so doubt we'll use the car much. We're just bringing it because it's something less to buy when we get there.. Plus we will use it eventually, with and two young kids, they'd be lost without it. Looking forward to the formalities of import and insurance etc.

Never thought about the plage, just along the road, possibilities.

That's why I mention the plage. But you need to check the price of parking your car there every day. 

Otherwise I'd probably look at areas that are easy to reach with busses 2 and 6 (the ones that go through Eaux-Vives, unless it changed recently). That way you can just hop on the bus to get to your car.