I know this is a highly controversial subject, and really impossible to discern in total, but perhaps we can come to a general ( all be it purely conjectured ) acknowledgement? I've been spending a lot of time pondering this, From real world information, and from in-universe information, I have come to the conclusion that it would have to be sometime in the very early 900's. For these reasons
1. "Icelandic Cod" is referenced in HTTYD1, and Iceland was Discovered by Naddoddur (Old Norse: Naddoðr) who came by it accidentally, and Hrafna-Flóki Vilgerðarson, who was the first to sail there intentionally and arrived in 868 AD. So, it would have to be around 900 AD for any trade route to be established.
2. No mention of christianity is made Throughout the entire series, implying it has no effect on the Berkians, or anyone in the barbaric archipelago. Denmark ( The first Scandinavian country to be Christianised ) Was Christianised in around 965 by Harald Bluetooth, as shown by the Jelling Runestone. so the franchise would have to be set earlier. However, Sweden wasn't fully converted until the early 13th century, so for an Archipelago North of Iceland, west of Svalbard, and East of Greenland, their traditions wouldn't be too hard to hide.
3. The Technology. In the Nine Realms, ( I haven't watched it, only seen clips ) looks very futuristic, so maybe it´s set a century and a bit in the future. ( Not that many people consider the Nine Realms canon mind you, but still ) may make the claim of 1,300 years since the Original franchise a little more plausible?
4. back to the point I made in #2, even if the Barbaric Archipelago weren't chrisitianised, there would probably be some sort of talk of the new religion to the south, if it was set in 1010AD as referred to in Racing for the gold, so I would definitely say set before 965 AD.
So, after my massive rant I have created instead of doing homework due in a few days, I have come to the conclusion that ( In my opinion ) the franchise was set in the early 900s, about 910 AD, 100 years prior than mentioned in Racing for the gold, due to the times, and the complete lack of knowledge of Archipelago-external happenings. So, Gobber would likely be born in 860, Stoick, born in 865, Valka born in 875, Hiccup, Astrid, and Snotlout born 895, and The Twins and Fishlegs born in 896. HTTYD 1 and Specials=910, RoB/DoB =911 RTTE and DotDR=913/14 HTTYD2= 915, HTTYDTHW=916, Zephyr born 918, Nuffink born 920/21 andHomecoming/Epilogue= 926 AD. I hope this was Semi-Helpful/related to HTTYD, and interesting at least. These were my thoughts anyway, pure conjecture. If you have other opinions I'd love to hear them! Thanks for enduring my rant :)