Note the OP wants a SMALL DIAMETER disc with same rim width. Rivers are a lot wider, both in diameter and rim (PDGA and westside list the Seer as 1.8cm but it is fact 1.6cm, verified by my fancy calipers).
When you get to 1.6cm rims you are pretty much limited to Leopard, Cheetah, Gazelle, Polaris, and JLS.
If you check out the Seer thread I have some pics up of my Tourney Seer next to a DX Cheetah. They look nearly identical, and fly as close as they look (the Seer may be a tad more stable though).
If you only want a tiny bit more stable try to find one of the early run Tourneys in dark blue (all the ones I saw were 172g or 173g). They are a lot less domey and have higher PLH than any of the dozens of VIP Seers I compared it to. Slightly again more stable would be a Millennium plastic Polaris LS. I have a really beat in one that flies like a Seer now but starts off more stable.
If you want more than just a touch more stable I would try out a Polaris in Sirius or Quantum. They fly a lot like a shorter Teebird and feel very similar to a Seer (they use the Cheetah top).
I also have a Champ Circle Stamp Cheetah and it is near Banshee stable and a lot shorter than my Seer when new but I am sure it would beat into something awesome if I just stuck to it.