Josh Homme used both a Peavey Standard, a Musician and various other PA's on Songs for the Deaf and Lullabies to Paralyze. The latter can be seen in this photo from this July 2005 Sound on Sound article, while the former is mentioned by Eric Valentine in this September 14, 2019 "Making Records with Eric Valentine" video at 30:45. The amp is shown in an October 29, 2001 photo at 31:38. Two can be seen in live in this BBC still and in this June 23, 2017 Instagram post.

So then, there's the main guitar and this was sort of an interesting moment in the guitar recording on the project because we had been using a bunch of crazy stuff, you know? Josh was primarily into using bass amps for his guitars and so we used these Ampeg V-4Bs that he brought in. That's what was used when we were tracking the band, tracking the basics with the band. And then we took this trip to Black Market Music and we got a bunch of just crazy, shitty old transistor Peavey amps. So they're like these Peavey Musician amps and stuff like that. I have some pictures that I can show you of the amps that illustrate that. [shows October 29, 2001 photo] So this is one of the miking setups, this was after... There was a moment when we had to leave Barefoot and go to another studio called The Site (...) So, these pictures are from that part of the session. This miking setup was probably used for the overdub guitar that you're gonna hear on this song ["No One Knows"]. But this right here, this is the V-4B. This is another Ampeg amp, this is a VT-40... and you can see it peekin' through, this is one o' these shitty Peavey transistor amps that we bought at Black Market. You can see it better here. Yeah, this is that Peavey. This was sort of our favorite. We bough two or three of these Peavey heads and this one sort of did the best.

It is also said that he used a Standard on Son's Of Kyuss and Wretch.

The amp is seen on top the stack on the right. This amp is also known to be used at their Polliwog Park gig.