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You can swap pretty much any B-series engine into a Civic using an automatic tranny. The 90-01 Integras were available with automatics, so you can use that transmission.
Honestly though, that transmission blows complete ass for performance purposes. It's definitely got the worst gearing of any B-series gearbox.
Automatic GS-R and B16 transmissions do exist, but they were never put in any car here in the States, so you'd have to talk to an engine importer to try and get one.
Is there some reason that the car needs to be automatic? You'd have a lot more fun with a manual B-series than one with a slushbox...