Elliptical orbit can definitely be a replacement for the lack of axial tilt.
While all other climate impacting factors, like ocean currents and air systems are able to create significant variations, they all ultimately depend on sun's energy. If this energy remains constant, it is difficult to imagine regular temperature fluctuations like we observe here on Earth (outside of equatorial latitudes).
Earth's orbit has an eccentricity of 0.0167. While this means that it is almost a circle, still there is a difference between perihelion and aphelion of 5 million km (147.1 vs 152.1). This translates to solar irradiation variation of 7% between the two points.
Axial tilt contributes much more than 7% to seasonal variations, in fact, it is unnoticeable that summers in southern hemisphere (that's when the Earth is in perihelion) are supposed to be warmer. Northern landmasses more than compensating for the difference, because land warms up faster than sea.
How much variation in solar energy do we need to have real seasons? According to this article, at the Cairo's latitude (30N) variation between summer and winter is 2 times. At London's latitude (51N), it is about 5 times. If we want to have a higher eccentricity orbit with no axial tilt, effect will be uniform for all of the planet.
Let's say we want the solar energy difference of 3 times. This means that the orbit must have aphelion to perihelion rate of SQRT(3) = 1.732, which will lead to eccentricity of 0.268
It also has to be noted that high eccentricity orbits have bodies travel faster in their perihelion than in aphelion. This means that winters on such planets will be longer than summers.