It probably makes the most sense to watch Death Billiards before Death Parade because it is a pilot episode and the TV series makes a passing reference to the bar customers from the movie. Chronologically speaking, the story of Death Billiards takes place sometime after episode 5 and before episode 10 of Death Parade.
If you take note of the roulette board in Death Billiards, it actually featured Chavvot. This roulette board was only switched in from the beginning of episode 5 of Death Parade at Nona's request. In the first four episodes of Death Parade (and in episode 6 at Ginti's bar), the roulette board only had a generic symbol on it.
The old woman who died and arrived at Quindecim in episode 10 of Death Parade was revealed to be the wife of the old man in Death Billiards, as shown on her set of cards and in her flashback. Also, during a flashback of the old man in Death Billiards, it was hinted that he passed away before his wife. Therefore, Death Billiards should occur before episode 10 of Death Parade.
@nhahtdh made a good argument that we could further restrict the occurrence of the events in Death Billiards to that before episode 8
if we take Chiyuki's mentality into consideration. She couldn't have been as relaxed as was shown at the end of Death Billiards if she had just sat through the trial of the two killers in episodes 8 and 9.
If you want to watch Death Billiards in between the Death Parade episodes, you should watch it after episode 6 and before episode 7 (or 8, the next best choice) because the only billiards game in Death Parade is played in episode 7, which lasted only about 90 seconds and commenced without any explanation to the rules of the game, so it would be a nice continuity to finish the movie first and then jump back to watch episode 7.
TL;DR: Watch Death Billiards either before episode 1 or in-between episodes 6 and 7 of Death Parade.