Tenant threatening to sue me for falling down stairs

[Matt Liu]

I inherited lousy tenants in a property (year lease) who are threatening to sue me for a slip down the stairs. She didn't seem injured but yadayada had to go to the doctors and did xrays yadayada. Now they're saying subtly (but really not so subtly) that if I can do "something" for them they won't have to press charges, otherwise, they will. In other words they want free pay day.

I have insurance but don't want to deal with the trouble and any rate change it may cause. Should I offer them cash to be quiet? Free rent for 2 months? Nice improvements to the unit? 

OR ... Should I threaten back very subtly that I can make things "less enjoyable" for them (and any ideas on that? Noise complaint warnings? No mercy with rent collection? Parking rules change?)? 

Thanks!!