The problem is going to be the existing stain and the possibility that pigment within will work through to the surface of the new finish.
Knowing whether the stain you have now is water-based or solvent-based is the key; and the only way of finding out is through trial and error. As a general rule, stains that migrate through a water based finish will not do so with a solvent based finish – and visa versa.
The first option is to paint over ‘as is’ with an opaque coloured wood stain such as Dulux Trade Ultimate Opaque. This is solvent based.
The alternative is Dulux Trade Quick Dry Opaque which is water based.
Both options will perform equally well although water based finishes tend to be more expensive but are much easier to use (especially over large areas).
Of course, any other brand will do, there just needs to be both options available. And, obviously, before committing yourself to a major purchase it will be worth your while doing a sample area first – just to be sure.
The other option would be to use a stain blocking primer like aluminium-based wood primer and finish with a conventional paint finish. Although this is an extreme measure that I would avoid if at all possible; opaque wood stains tend to last much longer than conventional paints and are much easier to maintain.