Coinstar’s Redbox business began 2010 by renting out more movie DVDs and Blu-ray discs in the first three months than Blockbuster — a major milestone cast as David toppling Goliath.

Nine months later, Blockbuster had gone belly up, and Redbox was second only to Netflix as a source of inexpensive movie rentals, solidifying its place as a dominant player in the U.S. home-entertainment market.

At the end of 2010, Redbox operated 30,200 self-service machines dispensing movie DVDs for a dollar a day at supermarkets, drugstores, fast-food restaurants and other places shoppers regularly visit. Redbox took in nearly $1.2 billion last year, accounting for 80 percent of Coinstar’s total revenue.

Bellevue-based Coinstar began buying into Redbox in 2005, when it was a fledgling McDonald’s venture, and took full ownership in 2009.

Although Coinstar has since sold businesses unrelated to Redbox and its namesake coin-counting machines, it continues to look for the next big thing in automated retail.

Redbox, for example, will add video-game rentals costing $2 a day to more than 21,000 locations nationwide by July 1.

Also, Coinstar has injected an undisclosed amount of money into ecoATM, a new venture that seeks to provide a convenient way for people to get cash for their old electronic devices, such as cellphones and iPods.

Still, whether 2011 has a happy ending for Coinstar could depend on what Redbox does next.

Some on Wall Street have grown impatient with Redbox’s indeterminate plans to introduce a video-streaming service on top of physical disc rentals.

In February, Redbox President Mitch Lowe told analysts the company was getting closer to finding an online partner for an unlimited streaming offer to take on Netflix. But the company has said only that full details will be released this year.