The German government today decided to introduce the €49 Germany Ticket on May 1. It is valid for one month on all local trains and buses nationwide (not on long-distance trains). It will be sold as a subscription, but can be cancelled monthly. This makes it attractive for visitors as well.
EDIT (04/18/23)
Since Deutsche Bahn sells the ticket only by SEPA direct debit (impracticable for visitors from non-SEPA countries) I have compiled a small list of other transport associations that accept payment by credit card or PayPal. I will try to keep it up to date and gladly include experiences of other forum participants.
VRN (Rhein-Neckar)
VRT (Trier)
Jelbi (Berlin)
MVV (München; Credit card, Apple Pay, Google Pay)
Mainzer Mobilität
VRS (Rhein-Sieg)
VBN (Bremen)
DVB (Dresden)
Deutschlandticket App (Not to be confused with the "Dein Deutschlandticket" app oder the website "Deutschlandticket.de", which don't accept CC oder PayPal)
EDIT June, 26
(1) I have deleted the reference to the hvv switch app from the list above because it does not seem to accept credit cards from overseas or direct debiting from accounts outside the EU even if they provide an IBAN. For Europeans it is still the most convenient app.
(2) The Man in Seat 61 now recommends the VBN app (previously the Mainzer Mobilität app) for overseas visitors. He offers a convenient step-by-step guide. What is lacking, however, is the following important hint: Keep the email with the booking confirmation, because it contains the link to the page where you can cancel. The app does not contain such a link (so far).
EDIT July, 12
There is now a reseller that allows the cancellation up to 24 hours before the end of the month: https://en.mopla.solutions/en/tickets/deutschlandticket
Beware of offers that prorate the first month's fee. According to updated federal regulations, this is only possible if you pay for the following month too, because the DT must be booked for at least one full month.