Hi Heksa!
I was considering answering your question earlier but just haven't got around to it. In a nutshell what you asking from the camera is beyond its capabilities. As Andy already mentioned your only option if you on't have an external flash is to increase the ISO. You can probably play around with various bounces from sunshade as Joye suggested but I haven't got much experience with those.
The way I would go about and what I did is to invest in external flash e.g. 420EX and then look at the wonderful accessories from Lumiquest http://www.lumiquest.com/
I've purchased the Pro-Max System http://www.wrotniak.net/photo/lq/index.html
directly from the Lumiquest and also picked up a copy of his "Flash…The MOST Available Light" http://www.lumiquest.com/ftmal.htm
while I was there. The results of course are not in the same league as professional (I am only using G2) but I am happy enough. Here is the shot of my nephew I shot a few weeks back:
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and another
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Both were shot with a window behind me and external flash at F2.8 1/60s no tripod and metered of the gray card. I've spot metered the scene of the same grey card in P mode to get the above exposure. I then went into manual mode and set it there manually.
Here is where you need to play with flash output. I was using a 20-80 Pocket Bounce from Lumiquest to bounce the external flash from the ceiling. In his book Q. Couch explains the relationship between flash and available (natural) light. Basicly at constant aperature changing shutter speed
only impacts on the portion of the image iluminated by available light and flash power settings
only impacts on the portion of the image iluminated by flash. Since like yourself I wanted the light to be more natural I wanted to reduce how much the scene is iluminated by the flash. Q. Couch suggest using 1 stop under available light exposure as a "balanced" fill flash. I then reduced the flash power output by 1 FEV. I could have lowered it further but since I was bounching it off the ceiling as well most of the flash would be diffused by it and I still would get 20% of it going straight on to give me those reflections in the eyes.
I shot those pics in RAW to give me the best possible option in terms of conversion and tweaking in PS CS. I used a BreezeBrowser to convert the RAW through linear conversion without any adjustment for saturation, shrpness or contrast. I then used Fred Miranda G2 LPBatch
http://www.fredmiranda.com/G2_LPbatch/
action to convert them in the PS CS (unfortunately I don't think he ever wrote any for other G-series cameras

). I tweaked the colours and sharpness in Photoshop and removed any noise that may have crept in through NeatImage.
Of course there are many other options and ways you can go about it since there is rarely one solution in photography. The above worked for me.
Good shooting
Flagpole
Sydney, Australia