Focus your effort on finding the right house for a great price. Leave the money in a bank account/CD to keep it available when needed.
Say you have $50,000 for a down payment. A 10% increase in stocks will generate $5,000 towards the down payment, but it may be a bumpy, stressful ride. By switching the hand-wringing into house hunting effort, you can easily save $5,000 on the purchase cost by taking the time to learn as much about the house buying market in your area.
I also second the barbell approach if you feel you must have some of it in stocks.