"(Last time they were primed and painted, the rain leaked(?) through and caused the latex paint to develop hanging bubbles of water (hanging down from porch planks.) So I am hesitant to put latex primer and paint on the underside of new bare wood again."

What are "hanging bubbles of water?"

Do you mean the water leaked through and dripped off the bottom?
That would be expected.

Well the rain got underneath / inside of the multiple coats of latex paint (rolled to the underside of the board) and caused the paint to stretch out and form a pocket full of water!

The latex paint streched out like a balloon and collected the water, so I had paint pockets filled with water hanging off the underside of my porch. (Which is the second floor entrance porch, so you could walk underneath and see what was happening.)

Any thoughts on eliminating this with a different kind of coating / sealer would be appreciated. Thanks.

How wet was the wood before painting?
If it was pressure treated it needs to dry out before painting since it gets saturated with water during treatment. That is why pressure treated wood is so heavy when purchased.

If the paint job was thorough, the next place to look is end grain.
It will soak up water and wick it into the wood a pretty decent distance.

For exterior wood that will be painted you can saturate the end grain with Minwax wood hardener till a gloss barely develops, then prime and paint.
It works very well on thinner sections that can rot and warp more.

I replaced 5 year old 1x6 corner boards on a house that had rotted at the butt joints between boards (3 stories on the back of the house).
After 15 years the replaced wood is still doing fine.