Channel coordination in search advertising is an important but complicated managerial decision for both manufacturers and retailers. Because of the highly concentrated market of search advertising, a manufacturer's and its retailers' ads can compete instead of complementing each other. We consider a manufacturer, who coordinates with its retailers by sharing a fixed percentage of each retailer's advertising cost and, at the same time, competes with its retailers and outside advertisers in search ad position auctions. Our model prescribes the optimal cooperative advertising strategies from the manufacturer's perspective. We find that different from cooperative advertising in traditional media, it can be optimal for a manufacturer to cooperate with only a subset of its retailers even if they are ex ante the same. This reflects the manufacturer's trade-off between higher demand and higher bidding cost caused by more intense competition. We also find that with two asymmetric retailers, the manufacturer should support the retailer with higher channel profit per click to get a higher position than the other retailer, which demonstrates the effectiveness of the participation-rate mechanism. The manufacturer should take a higher position than a retailer when its profit per click via direct sales exceeds the channel profit per click of the retailer. The main results still hold when we endogenize retail price competition or wholesale contracts.