There's very little round here or if there is, it's not advertised or mentioned online! I'm having to drive up to Rainford for the share I've found and round there it mostly seems to be DIY yards. The only horsey place in South Liverpool seems to be Beechley in Calderstones Park but I'm pretty sure that's just a riding school.
Seems to be lots of choice as you get further into Cheshire but very little in Liverpool itself. Unsurprising really as its so built up. Depending on which way you're happier driving then I'm sure you'll find somewhere on the Wirral/up the M57 towards Knowsley or Melling/out towards Runcorn and Widnes but you might be doomed to disappointment if you want something close to home.