That looks like white cedar to me. You could try copper napthenate. Google that! I had a hard time finding it but you can send away for it. Get a pump sprayer and coat the wood with it. It's a wood preservative. Also an insecticide and carpenter bees, ants, squirrels will avoid it. Only drawback is it has a strong creosote-ish odor that lingers for a long time, like forever. you can paint over it though. Keep it off your skin, it's hard to remove and it'll soak into ya.
I got Black Flag brand, it's green, but it can be found in brown too under the brand name Copper Brown I think.
Hurry before Hillary Cloton gives your land to the UN