Pushing implies forcing, and you shouldn't do this at all. Especially for tennis, which requires an intricate relationship with the sport though loss and victory.
Not sure what age you are talking about here. I would allow them to initially do many sports, and encourage all of them until they find one that they really enjoy. If its tennis, awesome! Its a great sport to learn and very social, with lifelong partnerships and an ability to teach sportsmanship, confidence, and commitment unlike any other sport.
As far as the IPADS/IPHONES, (and just because you asked, not judging here) if your off of them and have them put away your children will do the same. If not, thats your responsibility to enforce the standards.
Back to sport, if there is a true inclination of interest from your child in tennis, or another sport, share in the interest and help them realize/understand the effects of success and failure. In other words, don't beat them up if they have a bad match or day. Clap and cry with them. Make sure you understand the sport, be able to participate in it with them. I have seen parents just throw their child out there and not participate at all or try to understand what they are doing. If you sit on the sidelines and loosely have interest, they will feed on this and do the same, but also step far enough away you aren't just hanging over them on the court. its a balance you have to figure out. Help them to play a variety of matches so they win some and gain confidence. Tennis love is all about confidence, and a desire to overcome a defeat. If you are more upset or excited about your child's play then they are, they will only be playing for you. Just like anything in life you are there to encourage, train, and coach them. Sports are not a place for discipline.
So, no magic words to say to your child for them to have that ah ha moment, but rather like all things an life takes participation and commitment on your part. With almost all successful athletes you find several factors, but never was there a "pushing" success story.