Normally, if driving I'd avoid the Port Tunnel - it can be very expensive if you arrive at peak time. That being said, off-peak and on public holidays its a more reasonable €3. However, you'll have to pay a second toll to cross the East Link bridge (€1.90) when driving to Blackrock.
Another option is to take the M50 south to Junction 14 (Leopardstown) and head across to Blackrock via the N31. You'll still have to pay a toll on the M50 (but its less than the other two combined and you can pay this online). The M50 can be busy during rush hour, but at weekends/holidays its generally fine.
If you want to park on the north side and go by DART (check its schedule first to ensure there's no engineering works), then the DART station in Portmarknock has park and ride. There's some parking in Malahide too, but I don't know how many spaces there are there. Other stations have parking too so someone else may have other suggestions.