Use construction paper to draw/write whatever you want. (I wrote individual letters because we then used them to make words.) Cover the construction paper with clear contact paper for an instant play dough mat.
If you hate your kid playing with play dough, then here's some advice; you just need to get over it. Play dough is fun and kids like playing with it. And, it's great for strengthening their fine motor skills. I used to have this hang-up about doing messy crafts and activities when my son was a toddler, but I worked really hard at trying to let go of my anxiety with it. What's the worst thing that will happen? He'll get play dough on the floor? Oh well! It'll clean up. I still have to give myself a little pep talk every time we take out the "messy supplies."
Also, if you are like me and GAG at the smell of store-bought play dough, here's a great recipe for homemade playdough. Not only does it smell infinitely better, but you can make it to the texture/firmness that you want. My son has difficulty with play dough, because he has weak fine motor skills. We are working on strengthening the muscles in his hands to help improve his fine motor skills, so I make his play dough on the softer side. I'll firm up the next batch just a tad. Although it may be kind of a pain to make, this play dough lasts a long time in an airtight container. So, you can make a bunch at one time and it won't dry up like the store bough stuff.
I've also used this activity idea to make math play dough mats.
Embrace the mess and have fun!