$1 oysters daily, all night in the bar/lounge/patio area only (hat tip @dineLA)
Littlefork, 1600 Wilcox Ave, Los Angeles, CA 90028
$1 Naked Cowboy oysters daily, 5-7pm
EDIT: the deal is now $1.50 oyster of the day, daily 5-7pm and Friday&Saturday 10pm-close
Enterprise Fish Co, 174 Kinney St, Santa Monica, CA 90405
Mon-Sat, 4-7pm. Sunday 8-10pm, plus Fri-Sat 9-11pm
EMC Seafood & Raw Bar, 3500 W 6th St, Los Angeles, CA 90020
Daily 5-7pm
Green Hut Cafe, 808 W 7th St., Los Angeles, CA 90017
Daily after 3pm
Drago Centro, 525 S Flower St, Los Angeles, CA 90071
Daily, anytime on the bar menu, $5 for 4 Crystal Point oysters (OK so that's $1.25 each but pretty close and served with peach mignonette!)
Monday-Friday
Fickle, 362 E 1st St, Los Angeles, CA 90012
5-7PM (+$3 draft beers and $5 wines)
The Mercantile, 6600 Sunset Blvd, Los Angeles, CA 90028
5-8PM (+ happy hour drink specials)
Chaya Brasserie, 8741 Alden Dr, Beverly Hills, CA 90048
Chaya Venice, 110 Navy St, Venice, CA 90291
5-7pm in the bar/lounge/patio area
Sunday-Thursday
Faith and Flower, 705 W 9th St, Los Angeles, CA 90015
$1 oysters with pink peppercorn mignonette, 5-6:30pm. Bar/lounge area only.
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Monday
The Hungry Cat Santa Monica, 100 W Channel Rd (@PCH), Santa Monica, CA 90402
1/2 oysters all night (OK, technically not $1 but half off makes $7.50 for half dozen. Close enough)
Delphine, 6250 Hollywood Blvd, Hollywood, CA 90028
5-10:30pm ($1 East Coast oysters, $2 West Coast oysters)
Bar Marmont, 8171 W Sunset Blvd, West Hollywood, CA 90046
"Oyster at Cost Mondays" so the price will vary depending on the oyster, but supposedly they're no more than $1.50 each
Tipple and Brine, 14633 Ventura Blvd, Sherman Oaks, CA 91403
$1 oyster all night (4:30-11pm), bar/lounge/patio area
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Tuesday
MESSHALL, 4500 Hillhurst, Los Angeles, CA 90027
4-10pm (plus $5 beers)
Pearl's Liquor Bar, 8909 W Sunset Blvd, West Hollywood, CA 90069
5pm-until they run out
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Wednesday
McCormick and Schmick's, http://www.mccormickandschmicks.com/
5-10pm
The Churchill,
8384 W. 3rd St, Los Angeles, CA 90048
6pm-close (hat tip to LAist)
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Thursday
Cliff's Edge, 3626 W Sunset Blvd, Los Angeles, CA 90026
6-7pm ($20 for a dozen after)
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Friday
Caulfield's Bar and Dining Room, 9360 Wilshire Blvd, Beverly Hills, CA 90212
5-8PM
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Saturday-Sunday
Littlefork, 1600 Wilcox Ave, Los Angeles, CA 90028
$1 oyster of the day for brunch, 11am-3pm
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Sunday
BLVD16, 10740 Wilshire Blvd, Los Angeles, CA 90024
$1 oyster all day