How could I generate and automatically send customs reports by e-mail of Google Analytics to clients?

Actualy, there are good number of tools that can do it. ReportGarden, Marin, Data Graber, magic scripts by AdWords, hundreds of them... Problem is that lots of software gives you tremendous abilities but you have to learn how to use them correctly. Power brings responsibilities and AdWords calls to learnabilities. What if you don't have much time? Might be worth a look: http://foster.report/ is built for users with little programming background -- it pulls data from Google Analytics, generates custom reports and sends it to an email. Handy tool for PPC automation fueled by flexible algorithms.  

Antoine is absolutely correct. The best way is going to be to connect to the API via another tool - all the solutions in the above answer will work.  Essentially, what you do is "re-create" pieces of GA into another program / system (Excel will probably be your best bet) - once you begin pulling your GA data into Excel, you can start manipulating the data / format the sheet, and voila - you have a report you can brand / change / anything really - just remember, you need to set it up in a way that "auto-refreshes" or you're going to have manually update it every time you want to send the report. Lastly, you're going to have to figure out a way to automate it / send auto reports. I'd check out Google's Cloud Connect. Hope that helps!

You could use the Google Sheets Addon for Google Analytics (free) to pull the data and send links to the report online, or use one of the many online tools that serve that purpose (see the GA Partner Gallery for a list https://www.google.com/analytics/partners/search/apps?q=&category=111 ).If you want to use Excel, you can use a tool like Analytics Edge (http://www.analyticsedge.com/ ) that has a connector for GA, and can refresh reports and send emails on a schedule from your PC.

You should use http://www.tapanalytics.com/Being one of the top innovative digital marketing and reporting platform, features include: Automated Reporting - Export and schedule automatic reports into Email, Word, Excel, PDF and send them to clients Analytics Engine - Understand instantly when something needs attention or when to share success to your clients. Easy set-up - Get started in 30 seconds. Use the onboarding wizard to connect a tool, generate a dashboard, and schedule a report for one of your clients or stakeholders. Integrates with top analytic tools like Google Analytics, Boostability and Moz as well as social media platforms. You get more than what you ask for and a free trial is available.

We built a tool called ReportGarden(http://reportgarden.com) that can help you with this. You can combine data from google analytics, adwords and bing in your reports and schedule them to be emailed to your clients.

GA is very limited in this part, especially with customizing with logo. The best is to work with a 3rd party tool connected to GA's API like Canvas Analytics, Next Analytics, Bime, DigitalMidi. They'll allow you create the format you want and might have the feature to plan specific reports to specific users. They are all paid solutions. AT Internet that I represent is another analytics solution vendor, we offer that directly, might be work a look :)

http://megalytic.com is designed specifically for this purpose.  Report templates.  Highly customizable.  Add your own logos or cover pages.  Disclaimer:  I am a founder.