  Gravitationally lensed Type Ia supernovae (glSNe Ia) are unique astronomical
tools for studying cosmological parameters, distributions of dark matter, the
astrophysics of the supernovae and the intervening lensing galaxies themselves.
Only a few highly magnified glSNe Ia have been discovered by ground-based
telescopes, such as the Zwicky Transient Facility (ZTF), but simulations
predict the existence of a fainter, undetected population. We present a
systematic search in the ZTF archive of alerts from 1 June 2019 to 1 September
2022. Using the AMPEL platform, we developed a pipeline that distinguishes
candidate glSNe Ia from other variable sources. Initial cuts were applied to
the ZTF alert photometry before forced photometry was obtained for the
remaining candidates. Additional cuts were applied to refine the candidates
based on their light curve colours, lens galaxy colours, and the resulting
parameters from fits to the SALT2 SN Ia template. Candidates were also
cross-matched with the DESI spectroscopic catalogue. Seven transients passed
all the cuts and had an associated galaxy DESI redshift, which we present as
glSN Ia candidates. While superluminous supernovae (SLSNe) cannot be fully
rejected, two events, ZTF19abpjicm and ZTF22aahmovu, are significantly
different from typical SLSNe and their light curves can be modelled as
two-image glSN Ia systems. From this two-image modelling, we estimate time
delays of 22 $\pm$ 3 and 34 $\pm$ 1 days for the two events, respectively,
which suggests that we have uncovered a population with longer time delays. The
pipeline is efficient and sensitive enough to parse full alert streams. It is
currently being applied to the live ZTF alert stream to identify and follow-up
future candidates while active. This pipeline could be the foundation for glSNe
Ia searches in future surveys, like the Vera C. Rubin Observatory's Legacy
Survey of Space and Time.
