There was plenty ... when Skullgirls-on-console was brand-spankin'-new, eight years ago.
Now that the only "new" Skullgirls is last fall's Switch port and the ongoing development of SGM, merch is harder to come by, and what I've seen all looks to be on "once it's gone, it's gone" clearance.
Sanshee has a George plushie, cinema posters for half the original cast, and buttons for the entire 2E cast except Fukua and Robo. EightySixed has posters for Robo and Umbrella, Scribble Cat buttons, and a selection of keychains and T-shirts.
I've seen the soundtrack on Amazon and as a DLC for the Steam version of 2E.
If your after non-official (supports the product) items you could check out: http://www.redbubble.com
If you want a Plush? I' am not sure where to go, but this guy looks like he can self make it, and he seems the only one available?. Non-official again, link: https://mastodon.art/@Ultrapancake
I don't know how his sales rep is or anything, just a random search online.