There are so many factors involved in job hunting that it's natural to want to get every nitty gritty aspect right. While it's important to jump on a listing as soon as you can get your material together, there isn't any reason to get hung up on the time of day you submit your initial correspondence or application.
Each hiring manager will have his or her own process for reviewing the applications that come in and a set deadline for filling the position. It's more important to make sure your cover letter is flawless and that your correspondence is impressive than it is to be concerned with the time you submit it. On the off chance the hiring manager is the type of person who pays attention to the time you submit your application, sending an email early in the morning — as in between 6 and 9 a.m. — could be impressive because it says you are an enthusiastic early bird. That being said, make sure to keep the hiring manager's schedule in mind if you decided to make a follow-up call. In that case, call during business hours on a lower stress day of the week like Tuesday or Wednesday and plan what you will say in advance. Best of luck!