Almost anywhere in Thailand you will find a store that is open 24/7. There are 7-Eleven stores everywhere (8,469 stores across Thailand at the moment). They are always open and, of course, they stock condoms. Tesco Lotus is another big store chain with around 1,400 stores, and most of them are smaller Tesco Lotus Express stores that are open 24/7. Since 2013, Tesco Lotus also offers online shopping, so you can even order online or simply check what kind of products they sell and their prices.
Besides 7-Eleven and Tesco Lotus, the FamilyMart chain is also well represented in Thailand, and of course there are a lot of smaller family operated stores everywhere you go as well.
Another option is to purchase them at a pharmacy, and I found that the Watsons pharmacies have a particularly solid selection.
Big supermarkets, like Tops Market, will obviously also sell condoms, although the selection was pretty weak in one such supermarket that I visited.