The only results for which effect size estimates are currently produced in SPSS GLM are $F$ tests, for which you can get partial $\eta$2 values. Thus in order to get effect size estimates for these comparisons, you need to get them output as $F$ tests.
If the factor with three levels is one of the within-subjects factors, and you're looking at "main effects" comparisons (which are averaged over the levels of the other factors), you can simply use the contrast options to specify Simple contrasts and get two of the three comparisons at a time, changing the reference category on the second run to get the remaining comparison (i.e., run with Simple contrasts with the first category as the reference, then again with the last category as the reference, and all three of the distinct comparisons will be produced across the two runs). The "Tests of Within-Subjects Contrasts" output for contrasts on within-subjects factors shows $F$ tests for individual contrasts, so if you've requested effect size estimates to be shown, you'll get the partial $\eta$2 statistics.
If the three-level factor is the between-subjects factor, then in order to get $F$ tests for individual contrasts you'll need to use the
LMATRIX subcommand to specify each comparison among the levels of the factor desired (again, averaged over the levels of the other factors if nothing is done with the
MMATRIX subcommand). This requires using command syntax. You can set up the analysis in the dialog boxes, click the Paste button and add
LMATRIX subcommands like:
LMATRIX Valence 1 -1 0
LMATRIX Valence 1 0 -1
LMATRIX Valence 0 1 -1
and run the entire GLM command.