Something in Suburban Edinburgh not near the tram? Portobello?
Portobello isn't going to happen, mainly because you can't really do much without triggering a massive rebuilding.
The ideal solution would be putting a station where the old one used to be, near the bridge above Brighton place. Any station here would need a massive and expensive rebuilding of the two miles of ECML from Craigentinny Jn through to Portobello Jn, the bridges over Baileyfield Rd, and the end of the Borders line through to about Brunstane station.
Now, that probably isn't a bad thing in and of itself, that section probably needs a wholesale rebuilding to eek out capacity on the ECML into Waverley anyway, as it's basically at capacity as is; trains get into Waverley in whatever order they present themselves at Portobello Jn. There's not really much in the way of space for regulation. The Borders line is limited by the single lead junction, and single track through to Shawfair. The ECML lacks any regulation opportunity as far out as Dun bavr really, and you're limited to 1tph to North Berwick during weekday daytimes already. Craigentinny depot is a very busy place, and the sidings at Millerhill haven't helped in this regard.
If only we had an ECML route controller on the forums to give their insights onto this issue...
If you built a two platform station, the capacity hit on the ECML would kill it instantly, so you'd have to build some degree of station not dissimilar from Norton Bridge or Beaulieu Park, with an 'offline' platform off the main ECML running lines to stop services.
You have 3tph of potential services, upping to 4tph in the medium term: 2tph to the Borders and 1tph/2tph North Berwick services you could stop. If you're only stopping the former, then you may as well relocate Brunstane towards the junction and slew the ECML over, but what's the point? You could build a four platform station after the junction, but then you'd be messing around with overlaps and either taking a decent chunk of land from the depot, or again, realigning the two miles from Craigentinny to Joppa just to fit a station 200m from Brunstane.
Portobello is cursed by being close enough to the city centre that it should be the problem of TfE to speed up services, but far enough out that buses are very slow, especially at peak times.
The solution would be to remodel Portobello Jn through to Shawfair in a wholesale attempt to speed up services and increase capacity. If you do that, you could dual Brunstane station, increase the connectivity with buses, and turn it into a little transport hub, but you'd still be sending the good people of Portobello twenty minutes walk in the wrong direction to pick up 2tph to Edinburgh. I expect most people would stick with the 26 bus, no matter how busy it gets.