The correct method is to recaulk. If it has been a relatively dry year, thoroughly and repeatedly soak the deck down and keep it wet to allow it to swell. This alone may solve your leaks. Huron Pine will swell a great deal.
Another solution for pine and fir decks is to slop on the magic deck
oil. An excellent deck
oil recipe that has served me very well for decades. This should be repeated every six plus months or as needed. Recipe follows:
Mix in small batches in a deep pot, four
parts linseed oil, one part turpentine, and about one cup bee's wax per half gallon of mix. Slowly heat on a non-flaming burner, stirring, and monitoring closely. When the mix is hot enough to sizzle when a cotton rag is inserted remove from heat and apply to deck. Reheat every five minutes.
This hot deck oil will seep into the the seams and solidify. You should be leak free for many months. No need to sand between coats. Two coats minimum recommended. This mix will turn darker over time when exposed to sun light.
As foufou has suggested canvassing the deck is a good option. Sand the deck well if your fastener plugs are still long enough. Start midships and work towards the ends. Apply latex lagging
adhesive Looks like Elmer's or PVA glue generously to the deck. Lay a good quality canvass and squeegee the surface working to get out the air pockets. Let dry, apply another coat of
adhesive or
paint with several coats.