What would be a good alto instrument for a brass quartet? I'm simply transposing a piece into four parts for a brass quartet, but I can't think of a good brass alto instrument. I know french horn plays in the alto range, but would it sound brassier if I were to just have another trumpet play the alto part?

That's the tuba-player point of view, anyway.

Anyway, I think we can say that the brass quintet instrumentation is pretty standardized, whereas the brass quartet is not and that the brass quintet is a much more popular ensemble than the brass quartet.

Searching about in cyberspace I come up with multiple instances of three brass quartet instrumentations:

trumpet
trumpet
trombone
bass trombone

trumpet
trumpet
trombone
tuba

trumpet
trumpet
horn
tuba

I'm simply transposing a piece into four parts for a brass quartet

I think the word you want here is transcribing. Have you considered transcribing it for brass quintet? This might entail dividing a line between two instruments or adding a line. You'll have better luck getting the piece performed--or at least read through--if you write for a standard ensemble or a particular existing ensemble.

I know french horn plays in the alto range, but would it sound brassier if I were to just have another trumpet play the alto part?

Bear in mind that the trumpet is pretty weak at the bottom of its range. In its middle and high ranges the trumpet can easily overpower the horn in fortissimo passages, but if the piece stays piano to mezzo forte a horn would be a good choice if a true alto part is important.