In July and surrounding months much of Asia is hit by the "Southwest Monsoon", which brings rain on a near daily basis. Contrary to what some people suspect the Monsoon normally doesn't bring continuous rain, but is generally more common to have a single rain shower each day (normally in the afternoon). This rain can be extremely heavy, but depending on your exact travel plans is often not that difficult to plan around it.
However if you're after a country that avoids the monsoon, the best candidate is Indonesia. July is in the middle of the dry season there, with the wet season covering approximately October and April. On average it only gets rain on a few days in July. The catch is that July is also peak tourist season - in no small part due to the good weather!
Singapore gets rain pretty much year-round. July will have a little less rain than other months near the end of the year, but you can still expect some rain almost every other day.
Although not exactly South-East Asia, you could also try Turpan in China. July is actually one of it's wettest months of the year, but even so rainfall only averages 2mm for the entire month - and much of that evaporates before it actually hits the ground anyway! That said, if what you're after is good weather to go to the beach you're out of luck here - the nearest beach is about 2,500 km away.