I use a Guitarman GM11 Mini Tuner for all my stringed instruments including my autoharp. Clip it on to one of the pegs (not the one you are tuning) and move it when necessary. It is not perfect, but reasonably priced (mine cost me £15)and seemingly the battery lasts forever. (Well I have not had to change it yet and have had the tuner over three years to date.)
I have been playing autoharp for over 40 years, but recently a group of people here in the Isle of Man have taken an interest in the instrument and have got together with a couple of experienced lady harpers and we meet once a month and just jam together, picking up ideas as we go along. Great fun. I hope you have great fun with yours too. You might like to check out my autoharp playlist on my YouTube channel 'threelegsoman' where you will find examples of great harpers plus some of my own modest offerings.
Kind regards from the Isle of Man,