You should be able to get quite close at this time of year (northern hemisphere at least) because the fledglings aren't too keen on moving, and can't catch food for themselves, so you get lots of baby birds sat around whilst the parents desperately try and catch enough food for them as well as themselves, so they have to be bolder too.
Birds will get used to you too - the wild birds in places where lots of people go are less wary than in other places, so stick with it - eventually they'll get used to you being near.
This rather charming fledgling sparrow that was hanging around near the café at a butterfly house near me is an example of both these things - sitting around a lot being fed, and use to humans being near.
If you have room you might want to consider getting a tent or hide so you can get a different view point. I don't have a garden currently but I used to do bird watching from the shed when I was a kid.
Feed them regularly, let them get used to you, and try and get as close as you can.
You might also want to try trap focus is you have a MF lens. This was taken with a 25 year old Tamron Adaptall zoom. Not the greatest photo ever, but it shows it works, which was the reason I took it
EDIT - sparrow shot at 160mm (240mm in 35mm) to save you looking at the EXIF. The Robin was 210mm (315mm).