Julian didn't like tummy time either, but loved laying on my chest. We were also sure to do upper body exercises with him to help develop his muscles. He really enjoys it when I take his hands and cross them over his chest. This not only helps with upper body strength, but also with left/right brain development and him getting to know his body. We do a chant: "sat" when arms are out, "nam" when they cross.
My boy is only four months old, but the greatest thing I have learned in the last four months is that your baby will never do everything everyone says he should do. Tummy time three times a day might be great for some children, but you know your baby best and if he hates it then it sounds like you are doing a good job substituting!
One more thing - Julian used to hate tummy time, like I said above, but now he loves it! He learned how to roll over from back to front last week and now spends lots of time on his tummy! Be patient and it will come