Claire hated tummy time that age as well! I ended up just doing tummy time for her in short bursts, and usually on my chest so she could look at my face. I'd lie on the couch so my top half was elevated a bit and have her on my chest and make faces at her and sing her songs. She still wasnt keen on it, but she was happier to be on my chest that on a rug on the floor.
She was able to roll from her tummy to back around 3 months old so i dont think the lack of tummy time was a big problem for her.