For all our woodwork here we simply use white carpenters glue.
Then we clamp it for 48 hours - even though 24 will usually suffice.
One of the important things about gluing something together is the ability to knock it apart with a rubber mallet when it comes loose.
Sooner or late all glue needs to be replaced - use the wrong type and you end up damaging the wood.
In fact I put together an old maple rocking chair a couple of months or so ago - had to knock a few spindles out to clean everything and do a good job.
If I was refinishing it I would have just dumped the entire chair in the tank first to work all thed old glue off - but this was just a straight glue job.
If you value your chair and know that this job will be repeated in 5 - 10 - 15 years from now - be sure to use the right glue - or you may regret it.
If truly unsure, ask someone at your local refinishers shop - yellow pages - they will be happy to tell you what is available locally.
Bez>