Don't let them inbreed! I know many show bird keepers breed related birds to acheive a better shape/colour etc but I don't think anyone would advise it. Inbred chicks can have all sorts of problems ranging from deformities to behavioural problems. I have a breeding pair of kakarikis that I suspect may be related in some way - they have had two chicks now that just aren't quite right (hard to explain!). I won't be letting them breed again in the future. You can keep them living together if they're happy in each others company. Either don't give them a nest box or keep replacing the eggs with dummy eggs. If you want to breed tiels, take them apart and get them new mates. Hope that helps! ;D
I don't have tiels, so I don't know specifics of breeding, but if you do use dummy eggs, keep an eye on the hen. Breeding and laying mutiple eggs is hard on the hens, so if she just keeps trying to raise babies, you should probably remove the next box so she doesn't wear herself out.
Personally I would just not put a box in at all, but it is up to you. Hope everything works out!