What is a good savings rate for someone in their 30's and looking to save to buy a house in the next couple of years?

I generally suggest that people target an overall savings rate of 20%. Though you may need to target a higher percentage if you are just starting out saving in your 30s or something along those lines.

Within the scope of the overall rate, you can divide it up however you see fit.

As to the house issue, that is completely dependent on how much, if any, you currently have saved, the cost of the house you will buy, whether you want to put down 20% (in my opinion, you should strive to do so) or whether you are okay putting down less and paying PMI, etc.

Realistically, you can determine how much you want/need to put down, divide that by the number of months until you plan to buy a house and that is the monthly amount you will need to save.

But I would also suggest that you should not save exclusively for a home at the expense of saving for retirement and making sure that you work on building an emergency fund.