Make it about them
My tip is to make it about them as much as possible.
Butter them up and let them know you chose them and have done your research into them.
Be selective with the distributor you choose, you want them to have worked on films similar to yours, your genre or your sort of budget. Acknowledge this, tell them you have selected them because of the great work on XYZ project and think they have the necessary skills, qualities and enthusiasm to work with your film.
Tell them about your film quickly and concisely.
Are there particular contacts they have that you think would be beneficial to you and your film? Mention this:
"I see you have worked with XYZ who has a reputation for highlighting some excellent idie films in the past and I really think my film will resonate with them." People love to be on the insiders list for 'cool' things. Letting them get ahead of the curve is a great way to demonstrate the future potential of your working relationship.
The message wants to be pretty short but grabs their attention, think long term on this. You get their attention now and maybe they reply, in that next email you can let them know more, but for now leave a little mystery, just keep on that short but snappy line. And keep pushing the benefits in it for them.
You will go a lot of 'no's', keep racking them up. The more 'no's' the better I say, means your on the right path but just haven't found the person that really resonates with your film. They are out there and this is a test of persistence! It can be anywhere from about 10 'no's' to 1 'yes': JK Rowling 12 Nos and 1 yes, boom Harry Potter; Agatha Christie, 5 years of rejection and then one took it. Her book sales are now in excess of $2 billion. Only William Shakespeare has sold more.
Hope this helps!
Chris