The radiation comes from space in general, and not significantly from the sun, so a night flight has pretty much the same radiation level. 

However, unless you're flight crew or a frequent flyer or there's a solar storm going on, **radiation is not a significant problem.** You'll be bothered more by the cramped space and the airport routines. Get an aisle seat, and take occasional walks up and down the aisle. Also, drink water to counter the low humidity.

**[This page][1] contains the best Q&A about in-flight radiation concerns** I've found.  (Summary: It's generally safe.)

You can [use this online calculator][3] to determine how much radiation _your_ flight would bring.

To give you some perspective, [this chart][2] ([here's another][4]) shows that one flight across the USA brings you only 40 microsievert, which is one 25th of the yearly limit recommended by EPA, or just a few times more than a day's worth of background radiation on the ground. So if you fly 25 times in a year, you're still within reason. 

> Physicians can assure pregnant women who are concerned about radiation risks during flight that, for casual travel under normal solar conditions, the risk of direct
harm from cosmic radiation is negligible.  
...  
By referring to risk tables generated by [the FAA] and with knowledge of the recommended dose limits from national and international organizations concerned with
radiation safety, [pregnant flight crew members] can make an informed decision as
to the amount of flying that they wish to do. They should understand that these dose limits are set well below levels at which real harm has been demonstrated.

<sub>source: [In-Flight Radiation Exposure During Pregnancy (PDF)][5], American College of Obstetricians and Gynecologists.</sub>

> Radiation levels can be a lot higher, though, during solar flares — bursts of electromagnetic radiation caused by disturbances in the sun's atmosphere. Fortunately, solar flares are rare and last only a short while.  
The National Oceanic and Atmospheric Administration [posts solar radiation storm alerts on its web site][6]. Some experts recommend that pregnant women check the site before flying and consider postponing their trip a day or two if a storm is forecast.

<sub>source: [babycenter.com][7]</sub>


  [1]: http://www.hps.org/publicinformation/ate/faqs/pregnancyandflying.html
  [2]: http://www.informationisbeautiful.net/visualizations/radiation-dosage-chart/
  [3]: http://www.sievert-system.org/WebMasters/en/evaluation.html
  [4]: http://xkcd.com/radiation/
  [5]: http://www.acog.org/from_home/publications/green_journal/2004/v103n6p1326.pdf
  [6]: http://www.swpc.noaa.gov/SWN/index.html
  [7]: http://www.babycenter.com/404_will-the-radiation-im-exposed-to-on-an-airplane-flight-harm_1351065.bc