I don't have any experience with such things, however, if I was a tenant and then the new landlord wanted a security deposit from me, I would probably find it difficult to get you the money.
First, I would screen the tenants yourself. Legally, I don;t know what you can't or can do if they already live there, but it may be nice to know (if a tenant works at night and sleeps all day, for example).
Second, I would think of a creative way for them to get a security deposit. My first thought would be a "forced" saving plan. Something like, add $25/month to each rent check that would be added to their security deposit account. Once you reach that amount, they can continue with the current amount. Say, if they don't damage anything beyond a reasonable amount, they would get that lump sum back when they move out. Obviously, put this in writing and make sure they understand it. (While typing this, I was thinking about how you don't really know what damage they caused and the damage that was there before they moved in, so you might be out of luck for security deposits for these current tenants.)