We ended up at Oswald West in late August because it was the last weekend before school starting and we hadn't been on our beach trip yet -- Horrors! Our own Washington coast was forecast to have some serious rain so we headed to Oregon to try to avoid it. We were largely successful and had lovely sunshiny afternoons but it rained every morning from about 4 am to 10 am. Being the fair weather campers that we are, we didn't even have a tarp with us like the folks in my Accommodations tip picture.
So let this serve as a warning: It has been known to rain on the rainforest coast.
You should bring one or more blue tarps, a couple of poles to prop them up and plenty of rope to tie them down. One of the campsites near us looked like a domed stadium and those guys had no trouble staying dry while making breakfast.
For an up-to-date forecast check out the National Weather Service Portland Office.
If you get caught camping in the rain -- not unheard of on the rainforest coast -- you'll want to have access to a laundromat to run your and your kid's clothes through a dryer before you drive home. Luckily, your prayers are answered at the Cannon Beach RV Resort just off 101 at the Elk Creek Road exit in Cannon Beach.