Suppose it depends how one classes success. Sure, Labour going even more off the deep end coupled with Argentina winning the Falklands War probably means an Alliance government... but it's probably going to be disastrous, nigh-on impossible to govern, wiped out like the Lib-Dems in 2015 come the next election just a question of where the voters will go with practically everything being discredited. In that respect I wouldn't call the SDP/Alliance forming a government in 1983/4 following Labour and the Tories screwing the pooch a recipe for success.
If we were simply talking survival of the SDP or the Alliance and perhaps forming a Coalition partner in a government as success then that might be a bit more achievable without killing them off anyway a few years down the line. There's a possibility of a hung Parliament in the early 1990s, if you can avoid the merger of the Liberals and SDP that might help the Alliance retain a larger vote share but that perhaps helps the Tories more than Labour. You could avoid the merger if the Alliance does better in the 1987GE, they might do better if there isn't a fraught divide over defence between the Liberals and SDP in the run-up to that election. That might be less of an issue if the Alliance were not quite so wedded and there was more space between them, but to get that you really need to go all the way back to the start and perhaps have Roy go to the Liberals instead.
The issue is as well that there was probably a divide between the two parties over with whom to go into Coalition. Liberals might have preferred Labour, the SDP might have preferred the Tories. Perhaps a hung Parliament in an early 90s GE where the Alliance has not merged sees them split with the SDP joining the Tories as a junior partner in a Coalition. Would probably not serve them too well at whenever the next GE comes up, and might even split the party between Owen's Coalition SDP and a Maclennan/Kennedy Independent SDP! The latter would be especially interesting considering how much the Lib-Dems have maintained a presence in the Highlands thanks to the SDP practically absorbing most of the Labour membership there in the early 80s; though they may just merge with the Liberals eventually fun to imagine Highland Social Democrats sticking around!
As to Owen's continuity SDP, they did manage OTL to come second in the 1989 Richmond by-election that saw William Hague elected and that was ahead of the newly formed Liberal and Social Democrats. There's perhaps a chance they could even win. Kensington the year before and Vale of Glamorgan later the same year both saw the LSD finish ahead of the SDP, but could have maybe gone either way. They weren't really seen as a joke until the Bootle by-election in 1990 where they finished behind the Monster Raving Loony Party and, perhaps more embarrassingly, the continuity Liberals. It's actually relatively easy to have them survive, a win in Richmond, momentum lets them finish above the LSD in Vale of Glamorgan, maybe not have a spat between the MRLP and Labour gain the former a bit of attention so that the SDP finished above them and there isn't a move to wind-up.
They'd go into the 1992 GE with four MPs - Mike Potter in Richmond, John Cartwright in Woolwich, Rosie Barnes in Greenwich, and David Owen himself in Plymouth Devonport. Owen only announced his intention to stand down as an MP following winding up the Party, so might stick around since it was only at the request of Cartwright and Barnes that he stayed on as leader. Cartwright and Barnes managed decent performances OTL in 1992 as Independent Social Democrats, and with the SDP still in existence and David Owen not riding into the sunset yet they'd probably make it back. Don't think Potter has a chance though.
However, Owen is going sooner or later and when he does it's probably bye-bye for the SDP, especially if the Labour Party follows a similar trajectory in the 1990s as it did OTL.