Three separate arguments, taren. moving from specific to general.
Firstly, pg 145 of Magic of Faerun lists the Staff of Mighty Sweeping, a +2 sweeping quarterstaff qhich also gives the Improved trip Feat. Therefore Staves can be used to trip people.
Staves do not say in the PHB that they can be used to trip, therefore a weapon does NOT have to say it can be used to trip someone to be allowed to do so.
The logic problem here is this. The special weapons can be used to make trip attacks. the problem occurs when you therefore claim that only they can do this. reduced to absurdity this goes something like
Oranges are Fruit.
The book does not say that apples are fruit.
Therefore apples must not be fruit.
Lastly the Knockdown Feat (sword+fist) lets you trip "whenever you deal 10pts of damage in a melee." That is VERY inclusive, isnt it.
Therefore any weapon, or melee or dragons tail can be used trip.