Best Glue

Treated lumber is safe from mildew and insects when wet. It isn't protected from weather, or from moisture fluctuations, you want to STAIN IT for any kind of aboveground use.
Most good glues for outdoors are rigid and waterproof. Rigid is bad, because your wood will stretch/shrink in weather. A lot. The glue will crack. Waterproof, oddly, is bad too, because it will block movement of moisture. On dry days, your glue-wrapped tenon will still be swollen when the mortise it is in has shrunk, and the size mismatch causes wood to split. On wet days, the dry tenon will pull free of its glue joint as the mortise wood member swells.
I'd recommend a few dots of hot-melt glue. It's flexible, though somewhat weak, and won't wick on the wood to make any effective moisture barrier.
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