Ah, a simple single seat swing. Gotcha! All this while, I was
assuming a multi-seat porch type swing. Yep, almost any good plank
should do well for your seat. I would still suggest the most weather
resistant lumber, though, as it would likely be just as easy to
obtain as a non-weather resistant lumber. Those simple seats are easy
to change, if they go bad, also.

Neither of those trees aren't dispositioned enough that a swing's good/
proper motion would be affected. I would invest in eye bolts, as
initially recommended, hang and use the swing. If there are any
issues that arise, your installation/positioning is not so complicated
that any readjustment/reposition can't be done relatively easily.

In thinking porch swing (multi-person load bearing), I initially
though fairly heavy guage linked chain. Use your common sense for
chain size.... 1/8" guage.

Sonny