Wood knots have a tendency to weep sap as the wood cures, or dries. Paint reacts to sap like water reacts to oil. Oil and water aren't compatible. They don't blend. Before paint can bond properly to wood knots, the sap needs to be sanded away as much as possible and then blocked with a stain-blocking primer. The primer seals in the sap and allows a finish paint to bond to the primer. The primer also evens out the porosity difference between the knots and the surrounding wood. Knots can also be uneven in texture, so a wood putty should be applied before sanding begins.
Scoop a chunk of wood putty out of the tub with a putty knife and press the putty into the low areas of the knots until the putty is flush with the surrounding surface. Wait 24 hours for the putty to dry.
Sand the wood putty and any drops of sap weeping out of the knots with a 120-grit sanding black. Just move the sanding black back and forth over the knots with even downward pressure. Sand until the wood knots are flush with the surrounding surface of the wood.
Apply stain-blocking wood primer to the knots with a paintbrush. Move the brush bristles back and forth until coverage is achieved. Wait 24 hours and then paint over the primer coat with the finish paint.